Existence Solution and Controllability of Sobolev Type Delay Nonlinear Fractional Integro-Differential System

Hamdy M. Ahmed, Mahmoud M. El-Borai, Hassan M. El-Owaidy and Ahmed S. Ghanem
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Hamdy M. Ahmed: Higher Institute of Engineering, El-Shorouk Academy, P.O. Box 3, El-Shorouk City, Cairo, Egypt
Mahmoud M. El-Borai: Department of Mathematics, Faculty of Science, Alexandria University, P.O. Box 21515, Alexandria, Egypt
Hassan M. El-Owaidy: Department of Mathematics, Faculty of Science, Al-Azhar University, P.O. Box 11511, Cairo, Egypt
Ahmed S. Ghanem: Higher Institute of Engineering, El-Shorouk Academy, P.O. Box 3, El-Shorouk City, Cairo, Egypt

Mathematics, 2019, vol. 7, issue 1, 1-14

Abstract: Fractional integro-differential equations arise in the mathematical modeling of various physical phenomena like heat conduction in materials with memory, diffusion processes, etc. In this manuscript, we prove the existence of mild solution for Sobolev type nonlinear impulsive delay integro-differential system with fractional order 1 < q < 2 . We establish the sufficient conditions for the approximate controllability of Sobolev type nonlinear impulsive delay integro-differential system with fractional order 1 < q < 2 . In addition, we prove the exact null controllability of Sobolev type nonlinear impulsive delay integro-differential system with fractional order 1 < q < 2 . Finally, an example is given to illustrate the obtained results.

Keywords: Sobolev type delay nonlinear impulsive fractional integro-differential equations; resolvent operator; approximate controllability; null controllability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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