Hilfer and Hadamard functional random fractional differential inclusions

Saïd Abbas benchohra@univ-sba.dz
Mouffak Benchohra benchohra@univ-sba.dz
Jamal-Eddine Lazreg lagregjamal@yahoo.fr
Gaston M. N‘Guérékata gaston.n'guerekata@morgan.edu

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DOI:

https://doi.org/10.4067/S0719-06462017000100002

Abstract

This paper deals with some existence and Ulam stability results for some functional differential inclusions of Hilfer and Hilfer-Hadamard type with convex and non-convex right hand side. We employ some multi-valued random fixed point theorems for the existence of random solutions. Next we prove that our problems are generalized Ulam-Hyers-Rassias stable.

Keywords

Functional Random differential inclusion , left-sided Riemann-Liouville integral of fractional order , left-sided Hadamard integral of fractional order , Hilfer fractional derivative , convex , non-convex , Hilfer-Hadamard fractional derivative , existence , Ulam stability , random solution , fixed point

Saïd Abbas Laboratory of Mathematics, University of Saïda, P.O. Box 138, Saïda 20000, Algeria
Mouffak Benchohra Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abb`es 22000, Algeria.
Jamal-Eddine Lazreg Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abb`es 22000, Algeria.
Gaston M. N‘Guérékata Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore M.D. 21252, USA.

Pages: 17-38
Date Published: 2017-03-01
Vol. 19 No. 1 (2017): CUBO, A Mathematical Journal

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Published

2017-03-01

How to Cite

[1]

S. Abbas, M. Benchohra, J.-E. Lazreg, and G. M. N‘Guérékata, “Hilfer and Hadamard functional random fractional differential inclusions”, CUBO, vol. 19, no. 1, pp. 17–38, Mar. 2017.

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Vol. 19 No. 1 (2017): CUBO, A Mathematical Journal

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