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This paper investigates the dynamical semi-analysis of the delayed food chain model under the considered fractional order. The food chain model is composed of three compartments, namely, population of the prey, intermediate predator and a top predator. By using the fixed point theorem approach, we exploit some conditions for existence results and stability for the considered system via Atangana–Baleanu–Caputo derivative with fractional order. Also, using the well-known Adam–Bashforth technique for numerics, we simulate the concerning results for the interference between the prey and intermediate predator. Graphical results are discussed for different fractional-order values for the considered model. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to analyze a mathematical model for malware dissemination on wireless sensor networks with time delay. Local stability and exhibition of the Hopf bifurcation are explored by means of analysis of the distribution of roots of the consequential characteristic equation. Moreover, global exponential stability is established with the help of linear matrix inequality techniques. Furthermore, properties of the Hopf bifurcation such as the direction and stability are studied by utilizing the normal form theory and the center manifold theorem. Finally, a computer numerical simulation example is presented to certify the rationality of our obtained results. [ABSTRACT FROM AUTHOR]

This investigation aims to investigate the pine wilt disease model (PWDM) employing hybrid bio-inspired algorithm. The artificial neural networks-based genetic algorithm (ANNs-GA) as global search and sequential quadratic programming (SQP) serve as local search framework. The model consists of two populations, i.e. host (h) and vector (v). There are four classes in host population representing susceptible host (S h) , exposed host (E h) , asymptomatic host (A h) and infectious host (I h) whereas in vector susceptible (S v) and infectious (I v) class are present. Activation function is introduced for the formulation of the fitness-based function as mean squared error by using nonlinear PWD equations for the accomplishment of ANNs-GASQP paradigm. The stability, robustness and effectiveness of proposed paradigm is comparatively evaluated through Adam numerical scheme with absolute error analysis. Computational complexity of GASQP is determined by convergence criteria of best global weight, fitness evaluation, time, generations, iterations, function counts and mean square error. Moreover, the statistical analysis is performed via Theil's inequality coefficients (TICs), mean of absolute deviation (MAD) and root mean squared error (RMSE) for multiple trials of ANNs-GASQP. Results reveal that accuracy is obtained up to 3–11 decimal places which proves the reliability of proposed ANNs-GASQP solver. [ABSTRACT FROM AUTHOR]

In this paper, a new Meyer neuro-evolutionary computational algorithm is introduced for mathematical modeling of the epidemiological smoking model by employing hybrid heuristics of Meyer wavelet neural network with global optimized search efficiency of genetic algorithm and sequential quadratic programming. According to the World Health Organization, tobacco consumption kills 10% of all adults worldwide. The smoking epidemic is often regarded as the greatest health threat that humanity has ever confronted. So it's an important issue to address by employing hybrid suggested techniques. The Meyer wavelet modeling approach is exploited to describe the system model epidemiological smoking in a mean squared error-based function, and the systems are optimized using the proposed approach's combined optimizing capability. Root mean square error, Theil's inequality factor, and mean absolute deviation-based measurements are used to better verify the effectiveness of the suggested methodology. The combined approach for smoking model is verified, validated, and perfected through comparison investigations of reference results on stability, precision, convergence, and reliability criteria, which shows the novelty of this study. Furthermore, the results of the quantitative study support the value of the suggested approach-based stochastic algorithm. The values of absolute error lie between 1 0 − 2 and 1 0 2 , 1 0 − 6 and 1 0 − 3 , 1 0 − 6 and 1 0 − 4 , 1 0 − 6 and 1 0 − 3 , 1 0 − 5 and 1 0 − 4 , and 1 0 − 6 and 1 0 − 5 . The convergence measurement values for Theil's inequality coefficient lie between 1 0 − 5 and 1 0 0 , 1 0 − 1 0 and 1 0 − 5 , 1 0 − 1 0 and 1 0 − 5 , 1 0 − 1 0 and 1 0 − 5 , 1 0 − 1 0 and 1 0 − 5 , and 1 0 − 1 0 and 1 0 − 5 . [ABSTRACT FROM AUTHOR]

The main goal of this paper is to present a novel numerical scheme based on the Fibonacci wavelets for solving the brain tumor growth model governed by the Burgess equation. At the first instance, the Fibonacci-wavelet-based operational matrices of integration are obtained by following the well-known Chen–Hsiao technique. These matrices play a vital role in converting the said model into an algebraic system, which could be handled with any standard numerical method. To access the effect of medical treatment over the brain tumor growth, we have investigated both the linear and nonlinear cases of Burgess equation. The nonlinearity arising in the Burgess equation is handled by invoking the quasilinearization technique. In order to compare the efficiency of the Fibonacci-wavelet-based numerical technique, we formulated an analogous numerical scheme based on the Haar wavelets. Subsequently, both the methods are testified on several test problems and it is demonstrated that the Fibonacci wavelet method yields a much more stable solution and a better approximation than the Haar wavelet method. [ABSTRACT FROM AUTHOR]

In this paper, cubic polynomial and nonpolynomial splines are developed to solve solutions of 10th- and 12th-order nonlinear boundary value problems (BVPs). Such types of BVPs occur when a consistent magnetized force field is applied crosswise the fluid in the substance of gravitational force. We will amend our problem into such a form that converts the system of 1 0 th- & 1 2 th-order BVPs into a new system of 2 nd-order BVPs. The appropriate outcomes by using CP Spline and CNP Spline are compared with the exact root. To show the efficiency of our results, absolute errors calculated by using CP Spline and CNP Spline have been compared with other methods like differential transform method, Adomian decomposition method, variational iteration method, cubic B-spline, homotopy perturbation method, 5 th- and 6 th-order B-spline and our results are very encouraging. Graphs and tables are also presented in the numerical section of this paper. [ABSTRACT FROM AUTHOR]

In this paper, the analytic and fractional solutions of governing differential equations for helical flow of cylindrical nature have been presented. The series expansions and Laplace and Hankel transforms are applied to the governing equation of generalized Burger fluid flow for generating gamma functions. The analytical solutions of velocity fields and shear stresses are obtained through Caputo fractional approach. In order to justify the initial and boundary conditions, infinite series are invoked for expressing the analytical results of velocity fields and shear stresses in terms of H a , b + 1 1 , a (z) Fox-H function. At the end, few rheological parameters have been analyzed on four different types of models as shown in graphs. Finally, a comparative analysis of ordinary and fractional models has been focussed for angular and oscillating velocities of helical flow generated by circular cylinder. [ABSTRACT FROM AUTHOR]

There is no denying fact that helically moving pipe/cylinder has versatile utilization in industries; as it has multi-purposes, such as foundation helical piers, drilling of rigs, hydraulic simultaneous lift system, foundation helical brackets and many others. This paper incorporates the new analysis based on modern fractional differentiation on infinite helically moving pipe. The mathematical modeling of infinite helically moving pipe results in governing equations involving partial differential equations of integer order. In order to highlight the effects of fractional differentiation, namely, Atangana–Baleanu on the governing partial differential equations, the Laplace and Hankel transforms are invoked for finding the angular and oscillating velocities corresponding to applied shear stresses. Our investigated general solutions involve the gamma functions of linear expressions. For eliminating the gamma functions of linear expressions, the solutions of angular and oscillating velocities corresponding to applied shear stresses are communicated in terms of Fox- H function. At last, various embedded rheological parameters such as friction and viscous factor, curvature diameter of the helical pipe, dynamic analogies of relaxation and retardation time and comparison of viscoelastic fluid models (Burger, Oldroyd-B, Maxwell and Newtonian) have significant discrepancies and semblances based on helically moving pipe. [ABSTRACT FROM AUTHOR]

A current outbreak of the monkeypox viral infection, which started in Nigeria, has spread to other areas of the globe. This affects over 28 nations, including the United Kingdom and the United States. The monkeypox virus causes monkeypox (MPX), which is comparable to smallpox and cowpox (MPXV). The monkeypox virus is a member of the Poxviridae family and belongs to the Orthopoxvirus genus. In this work, a novel fractional model for Monkeypox based on the Caputo derivative is explored. For the model, two equilibria have been established: disease-free and endemic equilibrium. Using the next-generation matrix and Castillo's technique, if R 0 < 1 the global asymptotic stability of disease-free equilibrium is shown. The linearization demonstrated that the endemic equilibrium point is locally asymptotically stable if R 0 > 1. Using the parameter values, the model's fundamental reproduction rates for both humans and non-humans are calculated. The existence and uniqueness of the solution are proved using fixed point theory. The model's numerical simulations demonstrate that the recommended actions will cause the infected people in the human and non-human populations to disappear. [ABSTRACT FROM AUTHOR]

Recently, Atangana proposed new operators by combining fractional and fractal calculus. These recently proposed operators, referred to as fractal–fractional operators, have been widely used to study complex dynamics. In this paper, the COVID-19 model is considered via Atangana–Baleanu fractal-fractional operator. The Lyapunov stability for the model is derived for first and second derivative. Numerical results have developed through Lagrangian-piecewise interpolation for the different fractal–fractional operators. We develop numerical outcomes through different differential and integral fractional operators like power-law, exponential law, and Mittag-Leffler kernel. To get a better outcome of the proposed scheme, numerical simulation is made with different kernels having the memory effects with fractional parameters. [ABSTRACT FROM AUTHOR]

This paper will introduce novel techniques for a fractional-order model of the human liver involving the Atangana–Baleanu, Atangana–Toufik, and the Fractal fractional method with the nonsingular kernel. These techniques give more accurate and appropriate results. Existence and uniqueness have been developed with the help of fixed-point theory results. Numerical simulations are done from the developed algorithm of the model to elaborate the effect of fractional values and justify the theoretical results. Such kind of analysis will be useful for further investigation of epidemic diseases, and also provide a better understanding of disease dynamics to overcome the effect of disease in a community. [ABSTRACT FROM AUTHOR]

In the cultivation of Capsicum annuum (C. annuum), the major obstacles are triggered by the Yellow virus (Gemini virus). The virus is spread through insects, namely Bemisia tabaci (B. tabaci). To reduce the spreading of the virus in C. annuum, the entomopathogenic fungi (Verticillium lecanii) are used. We have analyzed the fractional-order model of chili plants with Atangana–Baleanu derivative (AB-derivative). Also, we calculate the numerical values to illustrate the results. [ABSTRACT FROM AUTHOR]

This paper is related to some qualitative results about the existence and uniqueness of a solution to a third-order problem by using a fixed point approach. Haar technique is applied for numerical solution of a third-order linear integro-differential equation (IDE) with initial conditions. In IDE, the third-order derivative is computed by Haar functions, and the integration is used to get the expression of second- and first-order derivatives, as well as an approximate solution. Some examples from the literature are used to verify the validity of the proposed method. Error analysis is performed. Also, comparison between the exact and numerical solutions at different collocation points (CPs) is derived. The convergence rate is recorded taking different numbers of CPs, which is approximately equal to 2. [ABSTRACT FROM AUTHOR]

A numerical method for the solution of nonlinear variable-order (VO) fractional differential equations (FDEs) is proposed in this paper. To determine the numerical solution of nonlinear VO FDEs, we used the Haar wavelet collocation method (HWCM) with a combination of Caputo fractional derivatives. For checking the efficiency of the HWCM, some examples are given. The maximum absolute error and mean square root errors of each test problem are computed for a different number of collocation points (CPs) to check the validity and applicability of the presented technique. The comparison of the exact and approximate solution is shown in figures for various numbers of CPs. [ABSTRACT FROM AUTHOR]

Fractional differential and integral equations are focus of the researchers owing to their tremendous applications in different field of science and technology, such as physics, chemistry, mathematical biology, dynamical system and engineering. In this work, a power series approach called Residual Power Series Method (RPSM) is applied for the solution of fractional (non-integer) order integro-differential equations (FIDEs). The Caputo sense is used for calculating fractional derivatives. Comparison of the obtained solution is made with the Trigonometric Transform Method (TTM) and Optimal Homotopy Asymptotic Method (OHAM). There is no restrictive condition on the proposed solution. The presented technique is simple in applicability and easily computable. [ABSTRACT FROM AUTHOR]

In this paper, we develop the theory of fractional order hybrid differential equations involving Riemann–Liouville differential operators of order ℓ ∈ (0 , 1). We study the existence theory to a class of boundary value problems for fractional order hybrid differential equations. The sum of three operators is used to prove the key results for a couple of hybrid fixed point theorems. We obtain sufficient conditions for the existence and uniqueness of positive solutions. Moreover, examples are also presented to show the significance of the results. [ABSTRACT FROM AUTHOR]

In the present paper, the optimal auxiliary function method (OAFM) has been extended for the first time to fractional-order partial differential equations (FPDEs) with convergence analysis. To find the accuracy of the OAFM, we consider the fractional-order KDV-Burger and fifth-order Sawada–Kotera equations as a test example. The proposed technique has auxiliary functions and convergence control parameters, which accelerate the convergence of the method. The other advantage of this method is that there is no need for a small or large parameter assumption, and it gives an approximate solution after only one iteration. Further, the obtained results have been compared with the exact solution through different graphs and tables, which shows that the proposed method is very effective and easy to implement for different FPDEs. [ABSTRACT FROM AUTHOR]