Initial-value problems for nonlinear hybrid implicit Caputo fractional differential equations

Abdelouaheb Ardjouni 1 * and Ahcene Djoudi 2

doi:10.26637/MJM0702/0026

Initial-value problems for nonlinear hybrid implicit Caputo fractional differential equations

Authors :

Abdelouaheb Ardjouni ^{1 *} and Ahcene Djoudi ²

Author Address :

¹ Department of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, Souk Ahras, 41000, Algeria.
² Faculty of Sciences, Department of Mathematics, University of Annaba, P.O. Box 12, Annaba 23000, Algeria.

*Corresponding author.

Abstract :

In this study, we use the contraction mapping principle to obtain the existence, interval of existence and uniqueness of solutions for nonlinear hybrid implicit Caputo fractional differential equations. We also use the generalization of Gronwall’s inequality to show the estimate of the solutions.

Keywords :

Implicit fractional differential equations, Caputo fractional derivatives, fixed point theorems, existence, uniqueness.

DOI :

10.26637/MJM0702/0026

Article Info :

Received : December 27, 2018; Accepted : May 17, 2019.