Displaying similar documents to “Ulam Stabilities for Partial Impulsive Fractional Differential Equations”

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...

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....

New existence and stability results for partial fractional differential inclusions with multiple delay

Saïd Abbas, Wafaa A. Albarakati, Mouffak Benchohra, Mohamed Abdalla Darwish, Eman M. Hilal (2015)

Annales Polonici Mathematici

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We discuss the existence of solutions and Ulam's type stability concepts for a class of partial functional fractional differential inclusions with noninstantaneous impulses and a nonconvex valued right hand side in Banach spaces. An example is provided to illustrate our results.

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.

Stability analysis of implicit fractional differential equations with anti-periodic integral boundary value problem

Akbar Zada, Hira Waheed (2020)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In this manuscript, we study the existence, uniqueness and various kinds of Ulam stability including Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability, and generalized Ulam-Hyers-Rassias stability of the solution to an implicit nonlinear fractional differential equations corresponding to an implicit integral boundary condition. We develop conditions for the existence and uniqueness by using the classical fixed point theorems such as Banach contraction...

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...