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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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

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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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Articles

Most read articles by the same author(s)

Mouffak Benchohra, Gaston M. N‘Guérékata, Djamila Seba, Measure of noncompactness and nondensely defined semilinear functional differential equations with fractional order , CUBO, A Mathematical Journal: Vol. 12 No. 3 (2010): CUBO, A Mathematical Journal
Mouffak Benchohra, Naima Hamidi, Fractional Order Differential Inclusions via the Topological Transversality Method , CUBO, A Mathematical Journal: Vol. 13 No. 2 (2011): CUBO, A Mathematical Journal
Mouffak Benchohra, Omar Bennihi, Khalil Ezzinbi, Existence Results for Some Neutral Partial Functional Differential Equations of Fractional order with State-Dependent Delay , CUBO, A Mathematical Journal: Vol. 16 No. 3 (2014): CUBO, A Mathematical Journal
Khalida Aissani, Mouffak Benchohra, Nadia Benkhettou, On Fractional Integro-differential Equations with State-Dependent Delay and Non-Instantaneous Impulses , CUBO, A Mathematical Journal: Vol. 21 No. 1 (2019)
Mouffak Benchohra, Fatima-Zohra Mostefai, Weak Solutions of Fractional Order Pettis Integral Inclusions with Multiple Time Delay in Banach Spaces , CUBO, A Mathematical Journal: Vol. 15 No. 1 (2013): CUBO, A Mathematical Journal
Nadjet Abada, Mouffak Benchohra, Hadda Hammouche, Existence Results for Semilinear Differential Evolution Equations with Impulses and Delay , CUBO, A Mathematical Journal: Vol. 12 No. 2 (2010): CUBO, A Mathematical Journal
Abdelhamid Bensalem, Abdelkrim Salim, Bashir Ahmad, Mouffak Benchohra, Existence and controllability of integrodifferential equations with non-instantaneous impulses in Fréchet spaces , CUBO, A Mathematical Journal: Vol. 25 No. 2 (2023)
Fatima Si bachir, Saïd Abbas, Maamar Benbachir, Mouffak Benchohra, Gaston M. N‘Guérékata, Existence and attractivity results for \(\psi\)-Hilfer hybrid fractional differential equations , CUBO, A Mathematical Journal: Vol. 23 No. 1 (2021)
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Svetlin Georgiev, Mohamed Majdoub, Two nonnegative solutions for two-dimensional nonlinear wave equations , CUBO, A Mathematical Journal: Vol. 24 No. 3 (2022)
N. Seshagiri Rao, K. Kalyani, Kejal Khatri, Contractive mapping theorems in Partially ordered metric spaces , CUBO, A Mathematical Journal: Vol. 22 No. 2 (2020)
Binayak Choudhury, Subhajit Kundu, Approximating a solution of an equilibrium problem by Viscosity iteration involving a nonexpansive semigroup , CUBO, A Mathematical Journal: Vol. 15 No. 3 (2013): CUBO, A Mathematical Journal
Leigh C. Becker, Uniformly Continuous ð¿¹ Solutions of Volterra Equations and Global Asymptotic Stability , CUBO, A Mathematical Journal: Vol. 11 No. 3 (2009): CUBO, A Mathematical Journal
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You may also start an advanced similarity search for this article.