EXISTENCE AND STABILITY RESULTS FOR GENERALIZED FRACTIONAL DIFFERENTIAL EQUATIONS

doi:10.1007/s10473-020-0110-3

Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (1): 141-154.doi: 10.1007/s10473-020-0110-3

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EXISTENCE AND STABILITY RESULTS FOR GENERALIZED FRACTIONAL DIFFERENTIAL EQUATIONS

A. BEN MAKHLOUF^1,2, D. BOUCENNA³, M. A. HAMMAMI²

1. Department of Mathematics, College of Sciences, Jouf University, Aljouf, Saudi Arabia;
2. Department of Mathematics, Faculty of Sciences of Sfax, Route Soukra, BP 1171, 3000 Sfax, Tunisia 3. Higher School for Professors of Technological Education, Skikda, Algeria

Received:2018-10-31 Revised:2019-02-04 Online:2020-02-25 Published:2020-04-14
Contact: A. BEN MAKHLOUF E-mail:benmakhloufabdellatif@gmail.com

Abstract

Abstract: In this paper, a sufficient conditions to guarantee the existence and stability of solutions for generalized nonlinear fractional differential equations of order α (1 < α < 2) are given. The main results are obtained by using Krasnoselskii's fixed point theorem in a weighted Banach space. Two examples are given to demonstrate the validity of the proposed results.

Key words: nonlinear fractional differential equations, stability analysis, generalized fractional derivative, Krasnoselskii's fixed point theorem

CLC Number:

26A33

A. BEN MAKHLOUF, D. BOUCENNA, M. A. HAMMAMI. EXISTENCE AND STABILITY RESULTS FOR GENERALIZED FRACTIONAL DIFFERENTIAL EQUATIONS[J].Acta mathematica scientia,Series B, 2020, 40(1): 141-154.

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EXISTENCE AND STABILITY RESULTS FOR GENERALIZED FRACTIONAL DIFFERENTIAL EQUATIONS

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