A coupled non-separated system of Hadamard-type fractional differential equations

Open Access

Original research article

Author(s):

Saleh S. Redhwan^a, Suad Y. Al-Mayyahi^b, Sadikali L. Shaikh^c, Mohammed S. Abd^d

^a Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004 (M.S.), India.
^b Department of Mathematics, College of Education for Pure Science, University of Wasit, Iraq.
^c Department of Mathematics, Maulana Azad College of Arts, Science and Commerce, Raza Bagh, Aurangabad 431004 (M.S.), India.
^d Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen.

Advances in the Theory of Nonlinear Analysis and its Applications 6(1), 33-44.

Received: April 26, 2021

Accepted: October 9, 2021

Published: October 12, 2021

Abstract

In this article, we discuss the existence and uniqueness of solutions of a coupled non-separated system for fractional differential equations involving a Hadamard fractional derivative. The existence and uniqueness results obtained in the present study are not only new but also cover some results corresponding to special values of the parameters involved in the Caputo problems. These developed results are obtained by apply-ing Banach’s fixed point theorem and Leray-Schauder’s nonlinear alternative. An example is presented to illustrate our main results.

Keywords: Hadamard-type fractional differential equations; Fixed point theorems; Boundary conditions.

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APA Style

Redhwan, S., Al-mayyahi, S., Shaikh, S., & Abdo, M. (2021). A coupled non-separated system of Hadamard-type fractional differential equations. Advances in the Theory of Nonlinear Analysis and its Application, 6(1), 33-44.