Existence and uniqueness of solutions for nonlinear implicit Caputo-Hadamard fractional differential equations with nonlocal conditions

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Original research article

Author(s):

Abdelouaheb Ardjouni^a, Ahcene Djouid^b

^aDepartment of Mathematics and Informatics, Souk Ahras University, P.O. Box 1553, Souk Ahras, Algeria
^bDepartment of Mathematics, Annaba University, P.O. Box 12, Annaba, Algeria

Advances in the Theory of Nonlinear Analysis and its Applications 3(1), 46-52.

Received: December 23, 2018

Accepted: March 24, 2019

Published: March 26, 2019

Abstract

In this paper, we apply the Banach fixed point theorem to establish the existence, interval of existence, and uniqueness of solutions for nonlinear implicit Caputo–Hadamard fractional differential equations with nonlocal conditions. Furthermore, we utilize a generalized form of Gronwall’s inequality to obtain estimates of the solutions.

Keywords: Implicit fractional differential equations, nonlocal conditions, Caputo–Hadamard fractional derivatives, fixed point theorems, existence, uniqueness.

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APA Style

Ardjouni, A., & Djoudi, A. (2019). Existence and uniqueness of solutions for nonlinear implicit Caputo-Hadamard fractional differential equations with nonlocal conditions. Advances in the Theory of Nonlinear Analysis and its Application, 3(1), 46-52.