CAPUTO FRACTIONAL INTEGRO-DIFFERENTIAL
EQUATION WITH NONLOCAL CONDITIONS
IN BANACH SPACE
Mohammed S. Abdo1, Abdulkafi M. Saeed2, Satish K. Panchal3
1,3Dr. Babasaheb Ambedkar Marathwada University
Aurangabad 431004 (M.S.), INDIA
2Dep. of Mathematics
College of Science
Qassim University
Buraydah 51452, SAUDI ARABIA

Abstract

The aim of the present paper is to prove the existence of solutions of the initial value problem for a nonlinear integro-differential equation of fractional order $\alpha \in (0,1)$ with nonlocal conditions in Banach spaces. The fractional differential operator is taken in the Caputo sense. The presented analysis relies on the Krasnoselskii's fixed point theorem. At the end, an illustrative example will be introduced to justify our result.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 32
Issue: 2
Year: 2019

DOI: 10.12732/ijam.v32i2.9

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