Hyers--Ulam and Hyers--Ulam Rassias stability of Caputo fractional linear differential equations

Alaa E. Hamza; Karima M. Oraby

doi:10.4134/CKMS.c240292

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Hyers--Ulam and Hyers--Ulam Rassias stability of Caputo fractional linear differential equations

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키워드

Caputo fractional integro-differential equations

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초록

In this paper, we obtain new sufficient conditions for the existence and uniqueness of solutions of Caputo fractional linear differential equations, via Banach fixed point theorem. Then, we investigate Hyers--Ulam and Hyers--Ulam--Rassias stability for such equations. Finally, two illustrative examples are given to show the applicability of the theoretical results.

Abstract

In this paper, we obtain new sufficient conditions for the existence and uniqueness of solutions of Caputo fractional linear differential equations, via Banach fixed point theorem. Then, we investigate Hyers--Ulam and Hyers--Ulam--Rassias stability for such equations. Finally, two illustrative examples are given to show the applicability of the theoretical results.

관련 논문AI추천

Global Existence and Ulam–Hyers Stability of Ψ–Hilfer Fractional Differential EquationsJyoti Pramod Kharade, Kishor Deoman Kucche경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2020 · 제60권 제3호 Nonlinear implicit fractional differential equation involving -Caputo fractional derivativeAHMED G. IBRAHIM, MOHAMMED S. ABDO, SATISH K. PANCHAL장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2019 · 제22권 제3호 Nonlocal boundary value problems for Hilfer fractional differential equationsAtthapol Kijjathanakorn, Jessada Tariboon, Sotiris K. Ntouyas, Suphawat Asawasamrit대한수학회 · 대한수학회보2018 · 제55권 제6호 A generalized approach of fractional Fourier transform to stability of fractional differential equationArusamy Mohanapriya, Periasamy Prakash, Varudaraj Sivakumar강원경기수학회 · 한국수학논문집2021 · 제29권 제4호 Uniqueness of solution for impulsive fractional functional differential equationPattani Samsudeen Sehik Uduman, Sandeep Singhal대한수학회 · 대한수학회논문집2018 · 제33권 제1호 Boundary value problems for differential equations of non-integer order involving Caputo fractional derivativeD.B.Dhaigude, J.A.Nanware장전수학회 · Advanced Studies in Contemporary Mathematics2014 · 제24권 제3호

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