Existence of integrable solutions for integro-differential inclusions of fractional order; coupled system approach

El-Sayed, A. M. A. ¹ ; Al-Issa, Sh. M. ²

¹ Faculty of Science, Alexandria University, Alexandria, Egypt
² Faculty of Science, Lebanes International University, Beirut, Lebanon;Faculty of Science, The International University of Beirut, Saida, Lebanon

Journal of nonlinear sciences and its applications, Tome 13 (2020) no. 4, p. 180-186.

Résumé

In this article, we establish the existence of solutions for a functional integral equation of fractional order. The study upholds the case when the set-valued function has $L^1$-Caratheodory selections, we reformulate the functional integral inclusion according to these selections via a classical fixed point theorem of Schauder and present theorem for the existence of integrable solutions. As an application, the existence of solutions of nonlinear functional integro-differential inclusion with an initial value, and the initial value problem for the arbitrary-order differential inclusion will be studied.

Détail

DOI : 10.22436/jnsa.013.04.02

Classification : 26A33, 47H30, 47G10
Keywords: Fractional calculus, integro-differential inclusion, \(L^1\)-Caratheodory selections, Schauder fixed point principle, Kolmogorov compactness criterion

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