Displaying similar documents to “New existence and stability results for partial fractional differential inclusions with multiple delay”

Ulam Stabilities for Partial Impulsive Fractional Differential Equations

Saïd Abbas, Mouffak Benchohra, Juan J. Nieto (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper we investigate the existence of solutions for the initial value problems (IVP for short), for a class of implicit impulsive hyperbolic differential equations by using the lower and upper solutions method combined with Schauder’s fixed point theorem.

Existence results of ψ-Hilfer integro-differential equations with fractional order in Banach space

Mohammed A. Almalahi, Satish K. Panchal (2020)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In this article we present the existence and uniqueness results for fractional integro-differential equations with ψ-Hilfer fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Mönch fixed point theorem and the Banach fixed point theorem. Furthermore, we discuss Eα-Ulam-Hyers stability of the presented problem. Also, we use the generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness...

A fixed point approach to the Mittag-Leffler-Hyers-Ulam stability of a fractional integral equation

Nasrin Eghbali, Vida Kalvandi, John M. Rassias (2016)

Open Mathematics

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In this paper, we have presented and studied two types of the Mittag-Leffler-Hyers-Ulam stability of a fractional integral equation. We prove that the fractional order delay integral equation is Mittag-Leffler-Hyers-Ulam stable on a compact interval with respect to the Chebyshev and Bielecki norms by two notions.

Hyers-Ulam stability of fractional linear differential equations involving Caputo fractional derivatives

Chun Wang, Tian-Zhou Xu (2015)

Applications of Mathematics

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The aim of this paper is to study the stability of fractional differential equations in Hyers-Ulam sense. Namely, if we replace a given fractional differential equation by a fractional differential inequality, we ask when the solutions of the fractional differential inequality are close to the solutions of the strict differential equation. In this paper, we investigate the Hyers-Ulam stability of two types of fractional linear differential equations with Caputo fractional derivatives....

Stability of Caputo fractional differential equations by Lyapunov functions

Ravi P. Agarwal, Donal O'Regan, Snezhana Hristova (2015)

Applications of Mathematics

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The stability of the zero solution of a nonlinear nonautonomous Caputo fractional differential equation is studied using Lyapunov-like functions. The novelty of this paper is based on the new definition of the derivative of a Lyapunov-like function along the given fractional equation. Comparison results using this definition for scalar fractional differential equations are presented. Several sufficient conditions for stability, uniform stability and asymptotic uniform stability, based...

An analysis of the stability boundary for a linear fractional difference system

Tomáš Kisela (2015)

Mathematica Bohemica

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This paper deals with basic stability properties of a two-term linear autonomous fractional difference system involving the Riemann-Liouville difference. In particular, we focus on the case when eigenvalues of the system matrix lie on a boundary curve separating asymptotic stability and unstability regions. This issue was posed as an open problem in the paper J. Čermák, T. Kisela, and L. Nechvátal (2013). Thus, the paper completes the stability analysis of the corresponding fractional...