Remarks on the fractional abstract differential equation with nonlocal conditions

Mohammed Benyoub; Samir Benaissa; Kacem Belghaba

doi:10.26637/MJM0704/0014

Abstract

In this paper, we study the existence and uniqueness of a solution to an initial value problem for a class of nonlinear fractional involving Riemann-Liouville derivative with nonlocal initial conditions in Banach spaces. We prove our main result by introducing a regular measure of noncompactness in the weighted space of continuous functions and using fixed point theory. Our result improve and complement several earlier related works. An example is given to illustrate the applications of the abstract result.

Keywords:

Riemann-Liouville fractional derivative, Riemann-Liouville fractional integral, nonlocal initial conditions, point fixed, measure of noncompactness

Mathematics Subject Classification:

Mathematics

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Mohammed Benyoub Department of Mathematics, University Djillali Liab`es of Sidi Bel-Abb`es, B.P.89, 22000, Sidi Bel-Abb`es, Algeria.
Samir Benaissa Department of Mathematics, University Djillali Liab`es of Sidi Bel-Abb`es, B.P.89, 22000, Sidi Bel-Abb`es, Algeria.
Kacem Belghaba Department of Mathematics, Laboratory of Mathematics and its applications, University of Oran1 A.B, 31000 Oran, Algeria.

Pages: 709-715
Date Published: 01-10-2019
Vol. 7 No. 04 (2019): Malaya Journal of Matematik (MJM)

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