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

Author

Listed:
  • Hind Hashem

    (Faculty of Science, Alexandria University, Alexandria 21526, Egypt
    Faculty of Science, Qassim University, Buraidah 51452, Saudi Arabia)

  • Ahmed El-Sayed

    (Faculty of Science, Alexandria University, Alexandria 21526, Egypt)

  • Dumitru Baleanu

    (Department of Mathematics, Cankaya University, Balgat, 06530 Ankara, Turkey
    Institute of Space Sciences, 077125 Magurele-Bucharest, Romania)

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.

Suggested Citation

  • Hind Hashem & Ahmed El-Sayed & Dumitru Baleanu, 2019. "Existence Results for Block Matrix Operator of Fractional Orders in Banach Algebras," Mathematics, MDPI, vol. 7(9), pages 1-9, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:856-:d:267934
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    References listed on IDEAS

    as
    1. Gao, Xin & Yu, Juebang, 2005. "Synchronization of two coupled fractional-order chaotic oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 141-145.
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