Journal of Applied Nonlinear Dynamics
A Nonlinear IntegroDifferential Equation with Fractional Order and Nonlocal Conditions
Journal of Applied Nonlinear Dynamics 9(3) (2020) 469481  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, AlHodeidah, Yemen
$^{3}$ Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad431001 (M.S), India
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Abstract
This paper deals with a nonlinear integrodifferential 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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