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The aim of this paper is to investigate the interpolative contractions involving rational forms in the framework of b-metric spaces. We prove the existence of a fixed point of such a mapping with different combinations of the rational forms. A certain example is considered to indicate the validity of the observed result. [ABSTRACT FROM AUTHOR]

In a recent paper (Filomat 32:4577–4586, 2018) the authors have investigated the existence and uniqueness of a solution for a nonlinear sequential fractional differential equation. To present an analytical improvement for Fazli–Nieto's results with some conditions removed based on a new technique is the main objective of this paper. In addition, we introduce an infinite system of nonlinear sequential fractional differential equations and discuss the existence of a solution for them in the classical Banach sequence spaces c 0 and ℓ p by applying the Darbo fixed point theorem. Moreover, the proposed method is applied to several examples to show the clarity and effectiveness. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to consider some F-contraction mappings in a dualistic partial metric space and to provide sufficient related conditions for the existence of a fixed point. The obtained results are extensions of several ones existing in the literature. Moreover, we present examples and an application to support our results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a new coupled system of fractional boundary value problems based on the thermostat control model. With the help of fixed point theory, we investigate the existence criterion of the solution to the given coupled system. This property is proved by using the Krasnoselskii's fixed point theorem and its uniqueness is proved via the Banach principle for contractions. Further, the Hyers–Ulam stability of solutions is investigated. Then, we find the approximate solution of the coupled fractional thermostat control system by using a numerical technique called the generalized differential transform method. To show the consistency and validity of our theoretical results, we provide two illustrative examples. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to investigate the existence, uniqueness, and Ulam–Hyers stability of positive solutions for fractional integro-differential boundary values problem. Uniqueness result is obtained by using the Banach principle. For obtaining two positive solutions, we apply another fixed point criterion due to Avery–Anderson–Henderson on cones by establishing some inequalities. An illustrative example is presented to indicate the validity of the obtained results. The results are new and provide a generalization to some known results in the literature. [ABSTRACT FROM AUTHOR]

The aim of this study is to introduce a new interpolative contractive mapping combining the Hardy–Rogers contractive mapping of Suzuki type and Z -contraction. We investigate the existence of a fixed point of this type of mappings and prove some corollaries. The new results of the paper generalize a number of existing results which were published in the last two decades. [ABSTRACT FROM AUTHOR]

In this paper, we propose two new contractions via simulation function that involves rational expression in the setting of partial b-metric space. The obtained results not only extend, but also generalize and unify the existing results in two senses: in the sense of contraction terms and in the sense of the abstract setting. We present an example to indicate the validity of the main theorem. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of solutions for a generalized sequential Caputo-type fractional neutral differential inclusion with generalized integral conditions. The used fractional operator has the generalized kernel in the format of (ϑ (t) − ϑ (s)) along with differential operator 1 ϑ ′ (t) d d t . We obtain existence results for two cases of convex-valued and nonconvex-valued multifunctions in two separated sections. We derive our findings by means of the fixed point principles in the context of the set-valued analysis. We give two suitable examples to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new quadratic functional equation and, motivated by this equation, we investigate n-variables mappings which are quadratic in each variable. We show that such mappings can be unified as an equation, namely, multi-quadratic functional equation. We also apply a fixed point technique to study the stability for the multi-quadratic functional equations. Furthermore, we present an example and a few corollaries corresponding to the stability and hyperstability outcomes. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlinear sequential q-difference equation based on the Caputo fractional quantum derivatives with nonlocal boundary value conditions containing Riemann–Liouville fractional quantum integrals in four points. In this direction, we derive some criteria and conditions of the existence and uniqueness of solutions to a given Caputo fractional q-difference boundary value problem. Some pure techniques based on condensing operators and Sadovskii's measure and the eigenvalue of an operator are employed to prove the main results. Also, the Ulam–Hyers stability and generalized Ulam–Hyers stability are investigated. We examine our results by providing two illustrative examples. [ABSTRACT FROM AUTHOR]

By using the classical fixed point theorem for operators on a cone, in this paper, some results of single and multiple positive solutions to a class of nonlinear first-order periodic boundary value problems of impulsive dynamic equations on time scales are obtained. It is worth noticing that the nonlinearity f and the pulse function in this paper are not positive. [ABSTRACT FROM AUTHOR]

In this paper we study fractional initial value problems with Caputo–Fabrizio derivative which involves nonsingular kernel. First we apply α-ℓ-contraction and α-type F-contraction mappings to study the existence and uniqueness of solutions for such problems. Finally, we use some contraction mappings in complete F -metric spaces for this purpose. [ABSTRACT FROM AUTHOR]

This paper provides two wide classes of contractions, which are obtained by using notions of α s p -admissibility and the rich set of C-class functions in the setting of a complete b-metric-like space under more general contractive conditions. An application is provided and many known results in the literature can be derived. [ABSTRACT FROM AUTHOR]

This paper is devoted to finding out some realization of the concept of b-metric like space. First, we attain a fixed point for two fuzzy mappings satisfying a suitable requirement of contractiveness. Subsequently, we apply such a result to graphic contractions. Also, we attain a unique solution for a system of integral equations, and lastly we give an application to ensure that there exists a common bounded solution of a suitable functional equation in dynamic programming. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the conditions on the control mappings ψ , φ : (0 , ∞) → R that guarantee the existence of the fixed points of the mapping T : X → P (X) satisfying the following inequalities: ψ (H (T x , T y)) ≤ φ (d (x , y)) ∀ x , y ∈ X , provided that H (T x , T y) > 0 , and ψ (H (T x , T y)) ≤ φ (A (x , y)) ∀ x , y ∈ X , provided that H (T x , T y) > 0 , where A (x , y) = max { d (x , y) , d (x , T x) , d (y , T y) , (d (x , T y) + d (T x , y)) / 2 } , and (X , d) is a metric space. The obtained fixed point results improve many earlier results on the set-valued contractions. As an application, we consider the existence of the solutions of an FDE. [ABSTRACT FROM AUTHOR]

In this paper, we study existence and uniqueness of solutions for a system of Hilfer–Hadamard sequential fractional differential equations via standard fixed point theorems. The existence is proved by using the Leray–Schauder alternative, while the existence and uniqueness by the Banach contraction mapping principle. Illustrative examples are also discussed. [ABSTRACT FROM AUTHOR]

By using the classical fixed point theorem for operators on a cone, in this paper, some results of one and two positive solutions to a class of nonlinear first-order periodic boundary value problems of impulsive dynamic equations on time scales are obtained. [ABSTRACT FROM AUTHOR]

Abstract In a recent paper (Filomat 32:4577–4586, 2018) the authors have investigated the existence and uniqueness of a solution for a nonlinear sequential fractional differential equation. To present an analytical improvement for Fazli–Nieto’s results with some conditions removed based on a new technique is the main objective of this paper. In addition, we introduce an infinite system of nonlinear sequential fractional differential equations and discuss the existence of a solution for them in the classical Banach sequence spaces c 0 $c_{0}$ and ℓ p $\ell_{p}$ by applying the Darbo fixed point theorem. Moreover, the proposed method is applied to several examples to show the clarity and effectiveness.

This paper is concerned with the existence of solutions for nonlinear fractional differential equations of Volterra type with nonlocal fractional integro-differential boundary conditions on an infinite interval. The results are obtained by using the Altman fixed point theorem. An example is presented in order to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, by using the Guo-Krasnoselskii theorem, we investigate the existence and nonexistence of positive solutions of a system of integral equation with parameters which can be seen as an effective generalization of various types of systems of boundary value problems for differential equation on continuous interval and time scales or fractional differential equations. We give a general approach of positive solutions to cover various systems of boundary value problems in a unified way, which avoids treating these problems on a case-by-case basis. Under some growth conditions imposed on the nonlinear term, we obtain explicit ranges of values of parameters with which the problem has a positive solution and has no positive solution, respectively. By giving some examples, we will show how our results may be applied to consider existence of positive solutions to a variety of system of boundary value problems of differential equations, differential equations on time scales or fractional differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of the solution of stochastic differential equation by means of the properties of the associated condensing nonexpansive random operator. Moreover, by taking account of the results of Diaz and Metcalf, we prove the convergence of Kirk's process to this solution for small times. [ABSTRACT FROM AUTHOR]

In this paper, the approximate controllability of partial neutral stochastic functional integro-differential inclusions with infinite delay and impulsive effects in Hilbert spaces is considered. By using Hölder's inequality, stochastic analysis and fixed point strategy with the properties of analytic resolvent operator, a new set of sufficient conditions is formulated, which guarantees the approximate controllability of the nonlinear impulsive stochastic system. The results are obtained under the assumption that the associated linear system is approximately controllable. An example is given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we discussed the existence of solutions for the fractional finite difference inclusion $\Delta^{\nu}x(t)\in F(t,x(t),\Delta x(t),\Delta^{2} x(t))$ via the boundary value conditions $\xi x(\nu-3)+\beta\Delta x(\nu -3)=0$, $x(\eta)=0$, and $\gamma x(b+\nu)+\delta\Delta x(b+\nu)=0$, where $\eta\in\mathbb{N}_{\nu-2}^{b+\nu-1}$, $2<\nu<3$, and $F:\mathbb {N}_{\nu-3}^{b+\nu+1}\times\mathbb{R}\times\mathbb{R}\times\mathbb {R}\to2^{\mathbb{R}} $ is a compact valued multifunction. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following two-point boundary value problem for q-fractional p-Laplace difference equations. New results on the existence and uniqueness of solutions for q-fractional boundary value problem are obtained. These results extend the corresponding ones of ordinary differential equations of integer order. Finally, an example is presented to illustrate the validity and practicability of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence and uniqueness of solutions for a differential equation of fractional-order $q \in(1, 2]$ subject to nonlocal boundary conditions involving Caputo derivative of the form $0 < \varrho_{1} < \sigma< \beta_{1} < \beta_{2} < \varrho_{2} <1$, $0<\mu<1$, and δ, a, b, c are real constants. We make use of some standard tools of fixed point theory to obtain the desired results which are well illustrated with the aid of examples. [ABSTRACT FROM AUTHOR]