Existence of integrable solutions for integro-differential inclusions of fractional order; coupled system approach
Volume 13, Issue 4, pp 180--186
http://dx.doi.org/10.22436/jnsa.013.04.02
Publication Date: January 08, 2020
Submission Date: August 26, 2019
Revision Date: October 31, 2019
Accteptance Date: November 27, 2019
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Authors
A. M. A. El-Sayed
- Faculty of Science, Alexandria University, Alexandria, Egypt.
Sh. M. Al-Issa
- Faculty of Science, Lebanes International University, Beirut, Lebanon.
- Faculty of Science, The International University of Beirut, Saida, Lebanon.
Abstract
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.
Share and Cite
ISRP Style
A. M. A. El-Sayed, Sh. M. Al-Issa, Existence of integrable solutions for integro-differential inclusions of fractional order; coupled system approach, Journal of Nonlinear Sciences and Applications, 13 (2020), no. 4, 180--186
AMA Style
El-Sayed A. M. A., Al-Issa Sh. M., Existence of integrable solutions for integro-differential inclusions of fractional order; coupled system approach. J. Nonlinear Sci. Appl. (2020); 13(4):180--186
Chicago/Turabian Style
El-Sayed, A. M. A., Al-Issa, Sh. M.. "Existence of integrable solutions for integro-differential inclusions of fractional order; coupled system approach." Journal of Nonlinear Sciences and Applications, 13, no. 4 (2020): 180--186
Keywords
- Fractional calculus
- integro-differential inclusion
- \(L^1\)-Caratheodory selections
- Schauder fixed point principle
- Kolmogorov compactness criterion
MSC
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