Existence results for nonlinear implicit fractional differential equations

Surveys in Mathematics and its Applications

Mouffak Benchohra¹  Jamal Eddine Lazreg² 

[1] Laboratory of Mathematics, University of Sidi Bel-Abbès, P. O. 89, Sidi Bel-Abbès 22000, Algérie and Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia ;Laboratory of Mathematics, University of Sidi Bel-Abbès, P. O. 89, Sidi Bel-Abbès 22000, Algérie;

关键词: Initial value problem;    Caputo's fractional derivative;    implicit fractional differential equations;    fractional integral;    existence;    Gronwall's lemma;    fixed point;   

DOI  :  

来源: DOAJ

【 摘 要 】

In this paper, we establish the existence and uniqueness of solution for a class of initial value problem for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, Schauder' fixed point theorem and the nonlinear alternative of Leray-Schauder type. As applications, two examples are included to show the applicability of our results.

【 授权许可】

Unknown