On a coupled system of fractional symmetric Hahn difference equations with nonlocal fractional symmetric Hahn integral boundary value conditions

In this paper, we propose a boundary value problems for fractional symmetric Hahn integrodifference equation. The problem contains two fractional symmetric Hahn difference operators and three fractional symmetric Hahn integral with different numbers of order. The existence and uniqueness result of problem is studied by using the Banach fixed point theorem. The existence of at least one solution is also studied, by using Schauder’s fixed point theorem.

In this article, we propose a coupled system of Caputo fractional Hahn difference equations with nonlocal fractional Hahn integral boundary conditions. The existence and uniqueness result of solution for the problem is studied by using the Banach’s fixed point theorem. Furthermore, the existence of at least one solution is presented by using the Schauder fixed point theorem.

This paper is concerned with the existence and uniqueness of solutions for a coupled system of Hadamard type fractional differential equations and integral boundary conditions. We emphasize that much work on fractional boundary value problems involves either Riemann-Liouville or Caputo type fractional differential equations. In the present work, we have considered a new problem which deals with a system of Hadamard differential equations and Hadamard type integral boundary conditions. The existence of solutions is derived from Leray-Schauder’s alternative, whereas the uniqueness of solution is established by Banach’s contraction principle. An illustrative example is also included.

This paper studies fractional differential equations (FDEs) with mixed fractional derivatives. Existence, uniqueness, stability, and asymptotic results are derived.

In this paper, we present some results for the attractivity of solutions for a k-dimensional system of fractional functional differential equations involving the Caputo fractional derivative by using the classical Schauder's fixed-point theorem. Also, the global attractivity of solutions for a k-dimensional system of fractional differential equations involving Riemann-Liouville fractional derivative are obtained by using Krasnoselskii's fixed-point theorem. We give two examples to illustrate our main results.

In this paper, we consider the existence and uniqueness for parametric boundary value problems of a coupled system of nonlinear fractional hybrid differential equations. By the fixed point theorem in Banach algebra, an existence theorem for parametric boundary value problems of a coupled system of nonlinear fractional hybrid differential equations is given. Further, a uniqueness result for parametric boundary value problems of a coupled system of nonlinear fractional hybrid differential equations is proved due to Banach's contraction principle. Further, we give three examples to verify the main results.

It is well known that Stochastic equations had many useful applications in describing numerous events and problems of real world, and the nonlocal integral condition is important in physics, finance and engineering. Here we are concerned with two problems of a coupled system of random and stochastic nonlinear differential equations with two coupled systems of nonlinear nonlocal random and stochastic integral conditions. The existence of solutions will be studied. The sufficient condition for the uniqueness of the solution will be given. The continuous dependence of the unique solution on the nonlocal conditions will be proved.

The following Reprint contains a total of 19 articles accepted and published in the Special Issue "Fractional Differential Equations, Inclusions and Inequalities with Applications II" of the MDPI journal Mathematics and covers various aspects of recent developments in the theory and applications of fractional differential equations, inclusions, inequalities, and systems of fractional differential equations and inclusions. Topics include, but are not limited to, the following themes: Oscillation for fractional-order differential equations, (p,q)-difference equations, q-difference inclusions, Integral inequalities, Fractional integro-differential equations, Sequential fractional differential equations, Sequential fractional differential inclusions, Numerical fractional differential equations, -fractional differential equations, Positive solutions for fractional boundary value problems, Stochastic fractional differential equations, Fractional-order systems, Caputo fractional differential equations, Delay difference equations, and BlackScholes fractional equations. In total, 80 manuscripts were submitted, and 19 papers by 68 authors from 21 countries were successfully published. It is hoped that the Reprint together with the ideas and publications therein will be of interest to readers and will inspire new studies on fractional differential equations, inclusions and inequalities.

As is known to all, Lipschitz condition, which is very important to guarantee existence and uniqueness of solution for differential equations, is not frequently satisfied in real-world problems. In this paper, without the Lipschitz condition, we intend to explore a kind of novel coupled systems of fuzzy Caputo Generalized Hukuhara type (in short, gH-type) fractional partial differential equations. First and foremost, based on a series of notions of relative compactness in fuzzy number spaces, and using Schauder fixed point theorem in Banach semilinear spaces, it is naturally to prove existence of two classes of gH-weak solutions for the coupled systems of fuzzy fractional partial differential equations. We then give an example to illustrate our main conclusions vividly and intuitively. As applications, combining with the relevant definitions of fuzzy projection operators, and under some suitable conditions, existence results of two categories of gH-weak solutions for a class of fire-new fuzzy fractional partial differential coupled projection neural network systems are also proposed, which are different from those already published work. Finally, we present some work for future research.

In this paper, we investigate the existence criteria of at least one positive solution to the three-point boundary value problems with coupled system of Riemann-Liouville type nonlinear fractional order differential equations. The analysis of this study is based on the well-known Schauder's fixed point theorem. Some new existence and multiplicity results for coupled system of Riemann-Liouville type nonlinear fractional order differential equation with three-point boundary value conditions are obtained.

Ordinary differential equations of fractional order have been presented as a tool of vital importance in modeling the anomalous dynamics of various problems from the exact sciences and engineering, however, is still under discussion a clear and coherent theory analogous to the classical theory of ordinary differential equations. The nonlocal character of their fractional operators provides additional information that allows the development of a comprehensive analysis of the mathematical models. Within these fractional order differential equations, the qualitative approach is an open topic of study at present, in which stability analysis plays a preponderant role. This article presents a description of recent results on the stability of nonlinear fractional order ordinary differential equations and some analytical methods used. First of all, this article presents and describes the fundamental concepts of the study of stability of systems of ordinary differential equations of fractional order, both linear and nonlinear. The results of this research provide fundamental tools in the study of the stability of systems of nonlinear fractional order differential equations that can be applied to various models of applied sciences and engineering. Keywords: fractional analysis, fractional differential equations, stability of fractional equations, Mittag-Leffler stability, Lyapunov functions. https://doi.org/10.55463/issn.1674-2974.50.7.7

In this article we study the a coupled system of fractional pantograph differential equations (FPDEs). Using degree theory, we state necessary conditions for the existence of solutions to a coupled system of fractional partial differential equations with non-local boundary conditions. Also using tools from non-linear analysis, we establish some stability results. We illustrate our theoretical results with a test problem. For more information see https://ejde.math.txstate.edu/Volumes/2020/132/abstr.html

In this research article, we investigate sufficient results for the existence, uniqueness and stability analysis of iterative solutions to a coupled system of the nonlinear fractional differential equations (FDEs) with highier order boundary conditions. The foundation of these sufficient techniques is a combination of the scheme of lower and upper solutions together with the method of monotone iterative technique. With the help of the proposed procedure, the convergence criteria for extremal solutions are smoothly achieved. Furthermore, a major aspect is devoted to the investigation of Ulam–Hyers type stability analysis which is also established. For the verification of our work, we provide some suitable examples along with their graphical represntation and errors estimates.

In this article, we study a coupled system of singular fractional difference equations with fractional sum boundary conditions. A sufficient condition of the existence of positive solutions is established by employing the upper and lower solutions of the system and using Schauder’s fixed point theorem. Finally, we provide an example to illustrate our results.

The main object of this paper is to investigate the existence of solutions for a self-adjoint coupled system of nonlinear second-order ordinary differential equations equipped with nonlocal multi-point coupled boundary conditions on an arbitrary domain. We apply the Leray–Schauder alternative, the Schauder fixed point theorem and the Banach contraction mapping principle in order to derive the main results, which are then well-illustrated with the aid of several examples. Some potential directions for related further researches are also indicated.