ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

A Nonlinear Integro-Differential Equation with Fractional Order and Nonlocal Conditions

Journal of Applied Nonlinear Dynamics 9(3) (2020) 469--481 | DOI:10.5890/JAND.2020.09.009

Hanan A. Wahash$^{1}$, Mohammed S. Abdo$^{2}$, Satish K. Panchal$^{3}$

$^{1}$ Research Scholar at Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India

$^{2}$ Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen

$^{3}$ Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad-431001 (M.S), India

Abstract

This paper deals with a nonlinear integro-differential equation of fractional order aϵ(0,1) with nonlocal conditions involving fractional derivative in the Caputo sense. Under a new approach and minimal assumptions on the function f , we prove the existence, uniqueness, estimates on solutions and continuous dependence of the solutions. The used techniques in analysis rely on fractional calculus, Banach contraction mapping principle, and Pachpatte's inequality. At the end, some numerical examples to justify our results are illustrated.

Acknowledgments

The authors are grateful to the referees for the careful reading of the paper and fortheir remarks.

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