Existence Results for Block Matrix Operator of Fractional Orders in Banach Algebras

Hind Hashem, Ahmed El-Sayed and Dumitru Baleanu
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Hind Hashem: Faculty of Science, Alexandria University, Alexandria 21526, Egypt
Ahmed El-Sayed: Faculty of Science, Alexandria University, Alexandria 21526, Egypt
Dumitru Baleanu: Department of Mathematics, Cankaya University, Balgat, 06530 Ankara, Turkey

Mathematics, 2019, vol. 7, issue 9, 1-9

Abstract: This paper is concerned with proving the existence of solutions for a coupled system of quadratic integral equations of fractional order in Banach algebras. This result is a direct application of a fixed point theorem of Banach algebras. Some particular cases, examples and remarks are illustrated. Finally, the stability of solutions for that coupled system are studied.

Keywords: fractional order operators; quadratic integral equations; coupled system; 2 × 2 block operator matrix (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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