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This paper is devoted to the study of Hyers–Ulam–Rassias (HUR) stability of a nonlinear Caputo fractional delay differential equation (CFrDDE) with multiple variable time delays. We obtain two new theorems with regard to HUR stability of the CFrDDE on bounded and unbounded intervals. The method of the proofs is based on the fixed point approach. The HUR stability results of this paper have indispensable contributions to theory of Ulam stabilities of CFrDDEs and some earlier results in the literature. [ABSTRACT FROM AUTHOR]

In this research, two systems of nonlinear Volterra integral equation and Volterra integro‐differential equation were considered. New results in sense of Ulam stabilities in relation to these two systems were proved on a finite interval. The proof of the results on the Ulam stabilities of that classes of the equations are based on the nonlinear alternative related to Banach's contraction principle. The outcomes of this research give new contribution to the theory of Ulam stabilities. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the sufficient conditions that guarantee the stability, continuity, and boundedness of solutions for a type of second-order stochastic delay integro-differential equation (SDIDE). To demonstrate the main results, we employ a Lyapunov functional. An example is provided to demonstrate the applicability of the obtained result, which includes the results of this paper and obtains better results than those available in the literature. [ABSTRACT FROM AUTHOR]

This article deals with the study of Hyers–Ulam stability (HU stability) and Hyers–Ulam–Rassias stability (HUR stability) for two classes of nonlinear Volterra integral equations (VIEqs), which are Hammerstein-type integral and Hammerstein-type functional integral equations, respectively. In this article, both the HU stability and HUR stability are obtained for the first integral equation and the HUR stability is obtained for the second integral equation. Among the used techniques, we present fixed point arguments and the Gronwall lemma as a basic tool. Two supporting examples are also provided to demonstrate the applications and effectiveness of the results. [ABSTRACT FROM AUTHOR]

In this work, we delve into a nonlinear integral equation (IEq) with multiple variable time delays and a nonlinear integro-differential equation (IDEq) without delay. Global existence and uniqueness (GEU) of solutions of that IEq with multiple variable time delays and IDEq are investigated by the fixed point method using progressive contractions, which are due to T.A. Burton. We prove four new theorems including sufficient conditions with regard to GEU of solutions of the equations. The results generalize and improve some related published results of the relevant literature. [ABSTRACT FROM AUTHOR]

In this study, we pay attention to a functional differential equation (FDE) of first order including N-variable delays. We construct new sufficient conditions in relation to the Hyers-Ulam stability (HUS) and the generalized Hyers-Ulam-Rassias stability (GHURS) of the FDE of first order including N-variable delays. By using Banach contraction principle (BCP), Picard operator and Gronwall's lemma, we confirm two new theorems with regard to the HUS and the GHURS. The results of this study are new, they extend and improve some earlier results of the HUS and the GHURS. [ABSTRACT FROM AUTHOR]

The authors deal with nonlinear and general Hammerstein-type functional integral equations (HTFIEs). The first objective of this work is to apply and extend Burton's method to general and nonlinear HTFIEs in a Banach space via the Chebyshev norm and complete metric. The second objective of the paper is to extend and improve some earlier results to nonlinear HTFIEs. The authors prove two new theorems with regard to the existence and uniqueness of solutions (EUSs) of HTFIEs via a technique called progressive contractions, which belongs to T. A. Burton, and the Chebyshev norm and complete metric. [ABSTRACT FROM AUTHOR]

This paper deals with the uniformly stability (US), globally uniformly asymptotically stability (GUAS) and instability of zero solution as well as integrability and boundedness of nonzero solutions of certain nonlinear integro‐differential equations (IDEs). We prove five new theorems, which include sufficient conditions related to these fundamental qualitative properties of solutions to the IDEs considered. The main tools used in the proof are two new and suitable Lyapunov–Krasovskiiˇ functionals (LKFs). In particular cases, two numerical examples are given and solved via the fourth order Runge–Kutta method (RKM) in MATLAB to illustrate the theoretical results of this paper. Compared with the existing results on the fundamental qualitative behaviors of scalar IDEs, our results are new, original, more effective and convenient for tests and applications. [ABSTRACT FROM AUTHOR]

In this paper, we consider a Hammerstein integral equation (Hammerstein IE) in two variables with two variables of time delays. The aim of this paper is to investigate the Hyers–Ulam (HU) stability and Hyers–Ulam–Rassias (HUR) stability of the considered IE via Banach's fixed point theorem (Banach's FPT) and the Bielecki metric. The proofs of the new outcomes of this paper are based on these two basic tools. As the new contributions of the present study, here, for the first time, we develop the outcomes that can be found in the earlier literature on the Hammerstein IE, including variable time delays. The present study also includes complementary outcomes for the symmetry of Hammerstein IEs. Finally, a concrete example is given at the end of this study for illustrations. [ABSTRACT FROM AUTHOR]

We consider a class of nonlinear second-order differential equations with constant delay and investigate qualitative properties of the solutions, namely, global stability of the zero solution, eventually uniform boundedness of solutions, existence of periodic solutions, and existence of a unique stationary oscillation of the considered equations. As far as the technique of the proofs is concerned, we use the Lyapunov–Krasovskii functional method and the second Lyapunov method to prove our main results. We also improve and correct some former results available from the literature. Finally, in some particular cases, we provide three examples as illustrations and applications of the obtained new results. Hence, we make some contributions to the topic of the paper. [ABSTRACT FROM AUTHOR]

In the paper "AIMS Math. 5 (2020), no. 6, 6448-6456", Tian et al. [15, Theorem 1] considered a linear system of integro-time delay differential equations (IDDEs) with constant time retardation. In [15], firstly, a generalized double integral inequality was obtained and then less conservative asymptotically stability criteria were proposed by using that double integral inequality and choosing a new Lyapunov-Krasovskii functional (LKF). To the best of the information, we would like to note that the asymptotically stability criteria of Tian et al. [15, Theorem 1] consist of very interesting but strong conditions. However, in this paper, we define a more suitable LKF, then we obtain the result of Tian et al. [15, Theorem 1] for uniformly asymptotically stability under very weaker conditions using the LKF and also investigate the integrability of the norm and boundedness of solutions. To show the effectiveness of our results, two numerical examples are proposed for the uniformly asymptotically stability as well as integrability and boundedness of solutions. By this work, we do contributions to the work of Tian et al. [15, Theorem 1] under very weaker conditions and those in the previous relevant literature, and we obtain two more new results on the integrability of the norm of solutions and boundedness of solutions. The results of this paper are new and they may be useful for researchers working on the topics of this paper. [ABSTRACT FROM AUTHOR]

In this article, a class of scalar nonlinear integro-differential equations of first order with fading memory is investigated. For the considered fading memory problem, we discuss the effects of the memory over all the values of the parameter in the kernel of the equations. Using the Lyapunov–Krasovski functional method, we give various sufficient conditions of stability, asymptotic stability, uniform stability of zero solution, convergence and boundedness, and square integrability of nonzero solutions in relation to the considered scalar nonlinear integro-differential equations for various cases. As the novel contributions of this article, the new scalar nonlinear integro-differential equation with the fading memory is firstly investigated in the literature, and seven theorems, which have novel sufficient qualitative conditions, are provided on the qualitative behaviors of solutions called boundedness, convergence, stability, integrability, asymptotic stability and uniform stability of solutions. The novel outcomes and originality of this article are that the considered integro-differential equations are new mathematical models, they include former mathematical models in relation to the mathematical models of this paper as well as the given main seven qualitative results are also new. The outcomes of this paper enhance some present results and provide new contributions to the relevant literature. The results of the article have complementary properties for the symmetry of integro-differential equations. [ABSTRACT FROM AUTHOR]

The authors of this paper examine uniformly asymptotically stability (UAS). uniformly boundedness (UB). ultimately uniformly boundedness (UUB) and existence of periodic solutions (EPSs) of certain nonlinear delay differential equations (DDEs) of third order with multiple constant delays. They prove two results and give a corollary on these properties of solutions. The main results of this paper have sufficient conditions and the technique of the proofs for these results is based on construction of a proper Lyapunov- KrasovskiT function (LKF). This paper has novel results to the theory of DDEs of third order and fills some gaps related to the mentioned concepts. [ABSTRACT FROM AUTHOR]

In this article, a scalar nonlinear integro-differential equation of second order and a non-linear system of integro-differential equations with infinite delays are considered. Qualitative properties of solutions called the global asymptotic stability, integrability and boundedness of solutions of the second-order scalar nonlinear integro-differential equation and the nonlinear system of nonlinear integro-differential equations with infinite delays are discussed. In the article, new explicit qualitative conditions are presented for solutions of both the second-order scalar nonlinear integro-differential equations with infinite delay and the nonlinear system of integro-differential equations with infinite delay. The proofs of the main results of the article are based on two new Lyapunov–Krasovskiĭ functionals. In particular cases, the results of the article are illustrated with three numerical examples, and connections to known tests are discussed. The main novelty and originality of this article are that the considered integro-differential equation and system of integro-differential equations with infinite delays are new mathematical models, the main six qualitative results given are also new. [ABSTRACT FROM AUTHOR]

In the present article, we study existence of periodic solutions (EPSs) of a nonlinear neutral integro-differential equation (NIDE) with multiple variable delays using Krasnoselskiis fixed point theorem. Transforming the considered NIDE to an equivalent integral equation, we prove the EPSs using a fixed point mapping, which is defined as a sum of a contraction and a compact map. The result of this paper has contributions to the topic of the EPSs of NIDEs. [ABSTRACT FROM AUTHOR]

In this article, admissibility problem for a kind of singular systems with delays is studied. Firstly, the given singular system with delays is transformed into a neutral system with delays. Secondly, new sufficient criteria are obtained on the stability of the new neutral system by aid of Wirtinger-based integral inequality, linear matrix inequality (LMI) and suitable Lyapunov-Krasovskii functionals (LKFs). The obtained criteria are valid for both of the systems. At the end, two numerical examples are given to illustrate the applicability of the obtained results using MATLAB-Simulink software. By this article, we extend and improve some results of the past literature. [ABSTRACT FROM AUTHOR]

This work studies certain perturbed and un-perturbed nonlinear systems of continuous and discrete integro-delay differential equations (IDDEs). Using the Lyapunov–Krasovskii functional (LKF) method and the Lyapunov–Razumikhin method (LRM), uniform asymptotic stability (UAS), uniform stability (US), integrability and boundedness of solutions as well as exponential stability (ES) and instability of solutions are discussed. In this paper, five new theorems and a corollary are given and three numerical applications are provided with their simulations. With this work, we aim to make new contributions to the theory of the continuous and discrete integro-differential equations. [ABSTRACT FROM AUTHOR]

We investigate the effect of pseudo symmetry. Ricci generalized pseudo symmetry, Ricci pseudo symmetry and Weyl projective pseudo symmetry conditions on submanifolds of conformal Kenmotsu manifolds provided that the Lee vector field either is normal to or has a non-zero tangential part on the submanifold and give a full classification of such submanifolds. Some new interesting and important results of this study are Einstein and mixed generalized quasi Einstein submanifolds and also some non-existence theorems of these types of submanifolds. Other results are a characterization of semi symmetric. Ricci semi symmetric and Weyl projective semi symmetric submanifolds with the same conditions on the Lee vector field. [ABSTRACT FROM AUTHOR]

This paper deals with a perturbed nonlinear system of fractional order differential equations (FrODEs) with Caputo derivative. The purpose of the paper is to discuss uniform stability (US), asymptotic stability (AS), Mittag-Leffer stability (MLS) of zero solution and boundedness at infinity of non-zero solutions of this perturbed nonlinear system of FrODEs with Caputo derivative. We obtain four new theorems on these mathematical concepts via a Lyapunov function (LF) and its Caputo derivative. For illustration, an example is provided which satisfies assumptions of the four new results and, in particular, shows their applications. The new results of this paper generalize and improve some recent ones in the literature and they have contributions to theory of FrODEs. [ABSTRACT FROM AUTHOR]

In the current work, we deal with a class of stochastic time-fractional integral equations in Hilbert space by studying their well-posedness and regularity. Precisely, we use the celebrity fixed point theorem to prove the well-posedness of the problem by imposing the global Lipschitz and the linear growth conditions. Further, we prove the spatial and temporal regularity by imposing only a regularity condition on the initial value. An important example is considered in order to confirm and support the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we summarize the local fractal calculus, called F α -calculus, which defines derivatives and integrals of functions with fractal domains of non-integer dimensions, functions for which ordinary calculus fails. Hyers–Ulam stability provides a method to find approximate solutions for equations where the exact solution cannot be found. Here, we generalize Hyers–Ulam stability to be applied to α -order linear fractal differential equations. The nuclear decay law involving fractal time is suggested, and it is proved to be fractally Hyers–Ulam stable. [ABSTRACT FROM AUTHOR]

In this study, we introduced a new type of basis function and subsequently a Chebyshev delta shaped collocation method (CDSC). We then use this method to numerically investigate both the natural convective flow and heat transfer of nanofluids in a vertical rectangular duct on the basis of a Darcy–Brinkman–Forchheimer model and the electroosmosis-modulated Darcy–Forchheimer flow of Casson nanofluid over stretching sheets with Newtonian heating problems. The approximate solution is represented in terms of Chebyshev delta shaped basis functions. Novel error estimates for interpolating polynomials are derived. Computational experiments were carried out to corroborate the theoretical results and to compare the present method with the existing Chebyshev pseudospectral method. To demonstrate our proposed approach, we also compared the numerical solutions with analytic solutions of the Poisson equation. Computer simulations show that the proposed method is computationally cheap, fast, and spectrally accurate and more importantly the obtained approximate solution can easily be used by researchers in this field. [ABSTRACT FROM AUTHOR]

In this work, we consider a nonlinear time-varying delay system of neutral type differential equations with periodic coefficients and we obtain new sufficient conditions to ensure exponentially stability of zero solution of this system. The Lyapunov-Krasovskii functional approach is useful as a basic tool to prove the main general result of this paper. [ABSTRACT FROM AUTHOR]

This paper deals with existence of w-periodic solutions of a nonlinear n-th order differential equation with variable delays. Some sufficient conditions related to w-periodicity of solutions were obtained by using coincidence degree theory. In a particular case, an application showing the accuracy of our results was given. [ABSTRACT FROM AUTHOR]

The paper deals with the problem of stabilizing the equilibrium states of a family of non-linear non-autonomous systems. It is assumed that the nominal system is a linear controlled system with periodic coefficients. For the nominal controlled system, a new method for constructing a Lyapunov function in the quadratic form with a variable matrix is proposed. This matrix is defined as an approximate solution of the Lyapunov matrix differential equation in the form of a piecewise exponential function based on partial sums of a W. Magnus series. A stabilizing control in the form of a linear feedback with a piecewise constant periodic matrix is constructed. This control simultaneously stabilizes the considered family of systems. The estimates of the domain of attraction of an asymptotically stable equilibrium state of a closed-loop system that are common for all systems are obtained. A numerical example is given. [ABSTRACT FROM AUTHOR]

In this article, a non-integer nonlinear mathematical model for toxoplasmosis disease in human and cat population is proposed and studied. The basic concepts of the model's dynamic are given. The study of qualitative dynamics is done by the basic threshold parameter R 0 . Local and global stabilities are done and the system's disease free equilibrium point is an attractor when R 0 < 1. Besides of it, endemic equilibrium point is an attractor when R 0 > 1. The sensitivity analysis of R 0 shows which parameter has positive/negative impact on the model. Numerical simulation of the model for the parameters occurred in threshold parameter is also discussed. The techniques of Adams Bashforth Moulton will be considered to justify all the derived theoretical results which will help in understanding to study the effect of various parameters to both the transient and steady-state dynamics of the disease infection. [ABSTRACT FROM AUTHOR]

In this manuscript, we review fractal calculus and random processes. Random variables and processes on totally disconnected fractal sets are defined. Random walks on fractal middle-ξ Cantor sets are suggested and corresponding variances are given which are power laws. The mean square stochastic calculus is generalized on fractal sets, which can lead to the standard case by setting dimension α = 1. Furthermore, we solve a fractal stochastic differential equation using the Frobenius method. Graphs are presented to give more details. [ABSTRACT FROM AUTHOR]

The concept of P-perturbed systems with respect to given system of ordinary differential equations is introduced. Certain sufficient conditions for uniform-ultimate Poisson boundedness of solutions of P-perturbed systems are obtained by using the method of Lyapunov functions. In conclusion, an interesting application of the above sufficient conditions to the standard closed electric RLC circuit with nonlinear elements is given. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlinear differential system of fractional-order with multiple variable delays. We investigate asymptotic stability of zero solution of the considered system. We prove a new result, which includes sufficient conditions, on the subject by means of a suitable Lyapunov functional. An example with numerical simulation of its solutions is given to illustrate that the proposed method is flexible and efficient in terms of computation and to demonstrate the feasibility of established conditions by MATLAB-Simulink. [ABSTRACT FROM AUTHOR]

In this paper, the stability (S), asymptotic stability (AS), uni- form stability (US) of null solution and boundedness of solutions of non-linear Volterra integro-differential equations (IDEs) are investi- gated by means of the Lyapunov-Krasovskii method (LKM). Four new theorems are provided on the mentioned concepts for the considered (IDEs). Compared with past related results in the literature, our conditions are simple, weaker and convenient for testing and applica- tions. The obtained results also improve and extend the past related results. Finally, two numerical examples are provided to illustrate the applications of our results. [ABSTRACT FROM AUTHOR]

The current research manifests kink wave answers, mixed singular optical solitons, the mixed dark-bright lump answer, the mixed dark-bright periodic wave answer, and periodic wave answers to the conformable fractional ZK model, including power law nonlinearity by plugging the revised (G ′ / G) -expansion process. The constraint requirements for the occurrence of substantial solitons are provided. Under the selection of proper values of a, b, n, t, λ, μ and α, the 2D and 3D pictures to a few of the recorded answers are sketched. From our obtained solutions, we might decide that the investigated procedure is hugely muscular, sincere, and essential in rendering various new soliton solutions of distinct nonlinear conformable fractional evolution equations and accordingly, we shall bring it up in our future investigations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate exponential stabilization problem for a class of linear systems with two continuous variable delays such that they belong to given intervals, but not necessary to be differentiable. By aid of a suitable Lyapunov-Krasovskii functional, Leibniz-Newton's formula and linear matrix inequalities (LMIs), we derive some new sufficient conditions for the exponential stability of the zero solution of the considered system. [ABSTRACT FROM AUTHOR]

In this paper, the existence and uniqueness and global exponential stability of almost periodic solutions are dis- cussed for a class of high-order fuzzy cellular neural net- works with time-varying delays. By means of some prop- erties of almost periodic functions, exponential dichotomy hypotheses and differential inequalities, certain suitable sufficient conditions are established to guarantee the exis- tence and uniqueness of solutions and exponential stabil- ity of solutions of the considered mathematical model. We prove two new results on the subject and give an example as an application of these results. [ABSTRACT FROM AUTHOR]

This study is concerned with the existence, uniqueness and global exponential stability of weighted pseudo almost periodic solutions of a generalized Nicholson’s blowflies equation with mixed delays. Using some differential inequalities and a fixed point theorem, sufficient conditions were obtained for the existence, uniqueness of at the least a weighted pseudo almost periodic solutions and global exponential stability of this solution. The results of this study are new and complementary to the previous ones can be found in the literature. At the end of the study an example is given to show the accuracy of our results. [ABSTRACT FROM AUTHOR]

Linear impulsive switched differential equations in Hilbert space are studied. We propose a new method of stability investigation, which is based in constructing an equivalent impulsive system without switching. Using operator-valued and scalar Lyapunov functions, sufficient conditions for Lyapunov stability of linear switched impulsive equations in a Banach space are established. The examples of studies of this class of equations with periodic switching are given. [ABSTRACT FROM AUTHOR]

In this work, the existence and uniqueness of solutions, boundedness of solutions and stability of zero solution of a specific neutral differential equations of first order with multiple time delays are discussed by the fixed point method. An example is given to show the applicability of the results introduced. By this work, we aim to extend and improve some previous results can be found in the literature and to do a contribution to the subject and the literature. [ABSTRACT FROM AUTHOR]

Abstract The Cη -Calculus includes functions on fractal sets, which are not differentiable or integrable using ordinary calculus. Sumudu transforms have an important role in control engineering problems because of preserving units, the scaling property of domains, easy visualization, and transforming linear differential equations to algebraic equations that can be easily solved. Analogues of the Laplace and Sumudu transforms in Cη -Calculus are defined and the corresponding theorems are proved. The generalized Laplace and Sumudu transforms involve functions with totally disconnected fractal sets in the real line. Linear differential equations on Cantor-like sets are solved utilizing fractal Sumudu transforms. The results are summarized in tables and figures. Illustrative examples are solved to give more details. [ABSTRACT FROM AUTHOR]

In this paper, we investigated the exponential stability for nonlinear neutral differential system with multiple retarded arguments. To reach the desired results, we used a Lyapunov-Krasovskii functional for exponential stability criterions of the zero solution of system. These stability criteria obtained are formulated as matrix inequalities which can be easily solved. The results obtained in this study extend and improves some related ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we relate with the stability, uniform stability, asymptotic stability, integrability and boundedness of solutions of a system of nonlinear differential equations of second order by the second method of Lyapunov. We obtain new sufficient conditions under which these properties of solutions of the equations considered are verified. Two examples are given to show the applicability of the results obtained and for illustrations. In the particular cases, the behaviors of the paths of that equations are exhibited by MATLAB-Simulink. The results of this paper extend and improve some results that can be found in the literature. [ABSTRACT FROM AUTHOR]

This work is devoted to investigate the stochastic asymptotically stability of the zero solution for a kind of third-order stochastic differentials equation with variable and constant delays by a suitable Lyapunov functional. Our results improve and form a complement to some results that can be found in the literature. In the last section, we give an example to illustrate our main result. [ABSTRACT FROM AUTHOR]

The influence of simultaneous variation of slip and temperature has been inquired for the case of free-convected flow of an MHD (magnetohydrodynamic), elastoviscous fluid past an unbounded upright plate. How the course of velocity is revamped in response to temperature alterations on boundary has been studied by considering two cases of constant temperature and variable temperature. The inverse and direct role of elastoviscous parameter (K), thermal Grashof number ( G r ) and Hartmann number (M) in determining the pattern of flow has been discussed through exact expressions and graphical illustrations. Interestingly, a G r -regime has been identified corresponding to elastoviscous velocity variation. The Newtonian fluid velocity past an unbounded plate entailing slip factor has also been retrieved and compared with elastoviscous fluid velocity. This comparative analysis reflects on magnitude and profile adaptations in response to numerical changes. [ABSTRACT FROM AUTHOR]

In this paper, we consider a non-linear stochastic differential delay equation (SDDE) of second order. We derive new sufficient conditions which guarantee stochastically stability and stochastically asymptotically stability of the zero solution of that SDDE. Here, the technique of the proof is based on the definition of a suitable Lyapunov-Krasovskii functional, which gives meaningful results for the problem under consideration. The derived results extend and improve some result of in the relevant literature, which are related to the qualitative properties of solutions of a SDDE of second order. The results of this paper are new and have novelty, and they do a contribution to the topic and relevant literature. As an application, an example is given to show the effectiveness and applicability of the obtained results. Finally, by the results of this paper, we extend and improve some recent results that can be found in the relevant literature. [ABSTRACT FROM AUTHOR]

The aim of paper is to analyse some qualitative properties of solutions of nonlinear Volterra integro-differential equations (VIDDEs) with constant delay and Volterra integro-differential equations (VIDEs) without delay by means of the Razumikhin method. A suitable Lyapunov function is defined and then applied to that IDEs such that some former results can be obtained under weaker conditions and additionally some new results are given on the qualitative properties of that IDEs such as uniformly stability and integrability of solutions. For the VIDDEs with constant delay, the improved less conservative conditions of the stability, asymptotically stability and the boundedness of solutions and the new conditions of uniformly stability, integrability of solutions are all derived subject to the functions appeared in the considered IDEs. Moreover, the established stability, asymptotically stability and boundedness conditions of VIDDEs with constant delay simplify, extend and improve some previous works can be found in the literature and remove some unnecessary conditions. Finally, the validity of the presented results is indicated by some numerical examples using MATLAB-Simulink. [ABSTRACT FROM AUTHOR]

This paper analyzes the stability, uniformly stability, asymptotically stability, boundedness, uniformly boundedness and square integrability of solutions of a system of differential equations of second order with variable delay by applying the direct method of Lyapunov- Krasovskii. By means of a new Lyapunov-Krasovskii functional, we simplify and extend some previous work that is found in the recent literature. Finally, the validity and applicability of the proceeded results are indicated by some numerical examples applying MATLAB-Simulink. By the results of this paper, we can obtain the results of Omeike et al. [Stability and boundedness of solutions of certain vector delay differential equations. J Nigerian Math Soc. 2018;37(2):77–87], Theorem 1.1 and Theorem 1.2, under weaker conditions. In addition, we establish two new results on the uniformly stability and integrabilty of solutions the considered equation. Finally, in particular cases, the applicability of the results of this paper can be shown by two new examples. These are the contribution of this paper to the subject and the relevant literature. [ABSTRACT FROM AUTHOR]

We consider a linear functional differential equation of first order and neutral type with multiple constant delays and present a functional Lyapunov approach to square integrability and asymptotic analysis of solutions of the equation considered. Consequently explicit criteria are derived for square integrability and asymptotic analysis of solutions of the equation considered. A discussion of the result obtained and an illustrative example are given. The result given extends and improves some found in the literature. [ABSTRACT FROM AUTHOR]

The main goal in this work is to establish a new and efficient analytical scheme for space fractional telegraph equation (FTE) by means of fractional Sumudu decomposition method (SDM). The fractional SDM gives us an approximate convergent series solution. The stability of the analytical scheme is also studied. The approximate solutions obtained by SDM show that the approach is easy to implement and computationally very much attractive. Further, some numerical examples are presented to illustrate the accuracy and stability for linear and nonlinear cases. [ABSTRACT FROM AUTHOR]

This paper is devoted to the instability of Set Differential Equations (SDEs). Using the geometric inequalities of Brunn–Minkowski and A.D. Aleksandrov, we propose new methods for constructing Lyapunov functions. In combination with the known methods of stability theory, the Lyapunov's direct method, the comparison method and the vector-function method, we establish conditions for the collapse of the solutions of the SDEs. Estimates of the collapse time of solutions are also obtained. Examples of SDEs in spaces of dimension 2 and 3 illustrating general theorems are given. [ABSTRACT FROM AUTHOR]

For a linear periodic system with impulsive action and delay, new approaches to the study of stability were proposed on the basis of the methods of spectral theory of linear operators, direct Lyapunov method, and N.G. Chetaev method for construction of the Lyapunov functions for the periodic linear systems, as well as the perturbation method for construction of the Lyapunov functions. These methods underlie the sufficient conditions for asymptotic stability of the linear periodic systems with impulsive action and delay. We gave some illustrative examples of studying stability of such systems under different assumptions about the dynamic properties of the continuous and discrete components of the impulsive system. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the existence of periodic solutions, stability of zero solution, asymptotic stability of zero solution, square integrability of the first derivative of solutions, and boundedness of solutions of nonlinear functional differential equations of second order by the second method of Lyapunov. We obtain sufficient conditions guaranteeing the existence of periodic solutions, stability of zero solution, asymptotic stability of zero solution, square integrability of the first derivative of solutions, and boundedness of solutions of the equations considered. We give an example for illustrations by MATLAB-Simulink, which shows the behaviors of the orbits. The findings of this paper extend and improve some results that can be found in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we use the Hahn integral operator for the description of new generalization of Minkowski’s inequality. The use of this integral operator definitely generalizes the classical Minkowski’s inequality. Our results with this new integral operator have the abilities to be utilized for the analysis of many mathematical problems as applications of the work. [ABSTRACT FROM AUTHOR]