Displaying similar documents to “Hyers-Ulam stability of fractional linear differential equations involving Caputo fractional derivatives”

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

Similarity:

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...

Ulam Stabilities for Partial Impulsive Fractional Differential Equations

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

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Similarity:

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.

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

Similarity:

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

Similarity:

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.

Fractional descriptor continuous-time linear systems described by the Caputo-Fabrizio derivative

Tadeusz Kaczorek, Kamil Borawski (2016)

International Journal of Applied Mathematics and Computer Science

Similarity:

The Weierstrass-Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor continuous-time linear systems described by the Caputo-Fabrizio derivative. A method for computing solutions of continuous-time systems is presented. Necessary and sufficient conditions for the positivity and stability of these systems are established. The discussion is illustrated with a numerical example.

Theorems on some families of fractional differential equations and their applications

Gülçin Bozkurt, Durmuş Albayrak, Neşe Dernek (2019)

Applications of Mathematics

Similarity:

We use the Laplace transform method to solve certain families of fractional order differential equations. Fractional derivatives that appear in these equations are defined in the sense of Caputo fractional derivative or the Riemann-Liouville fractional derivative. We first state and prove our main results regarding the solutions of some families of fractional order differential equations, and then give examples to illustrate these results. In particular, we give the exact solutions for...

A detailed analysis for the fundamental solution of fractional vibration equation

Li-Li Liu, Jun-Sheng Duan (2015)

Open Mathematics

Similarity:

In this paper, we investigate the solution of the fractional vibration equation, where the damping term is characterized by means of the Caputo fractional derivative with the order α satisfying 0 < α < 1 or 1 < α < 2. Detailed analysis for the fundamental solution y(t) is carried out through the Laplace transform and its complex inversion integral formula. We conclude that y(t) is ultimately positive, and ultimately decreases monotonically and approaches zero for the case...