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On Fractional Order Hybrid Differential Equations

Author

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  • Mohamed A. E. Herzallah
  • Dumitru Baleanu

Abstract

We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order . Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.

Suggested Citation

  • Mohamed A. E. Herzallah & Dumitru Baleanu, 2014. "On Fractional Order Hybrid Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, March.
    • Handle: RePEc:hin:jnlaaa:389386
    DOI: 10.1155/2014/389386
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    Cited by:

    1. Samina & Kamal Shah & Rahmat Ali Khan, 2020. "Stability theory to a coupled system of nonlinear fractional hybrid differential equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(2), pages 669-687, June.
    2. Sebastian Wolff & Svenja Kalt & Manuel Bstieler & Markus Lienkamp, 2021. "Influence of Powertrain Topology and Electric Machine Design on Efficiency of Battery Electric Trucks—A Simulative Case-Study," Energies, MDPI, vol. 14(2), pages 1-15, January.
    3. Zakir Ullah & Amjad Ali & Rahmat Ali Khan & Muhammad Iqbal, 2018. "Existence Results To A Class Of Hybrid Fractional Differential Equations," Matrix Science Mathematic (MSMK), Zibeline International Publishing, vol. 2(1), pages 13-17, January.
    4. Ahmed M. A. El-Sayed & Wagdy G. El-Sayed & Somyya S. Amrajaa, 2021. "On a Boundary Value Problem of Hybrid Functional Differential Inclusion with Nonlocal Integral Condition," Mathematics, MDPI, vol. 9(21), pages 1-16, October.
    5. Zidane Baitiche & Kaddour Guerbati & Mouffak Benchohra & Yong Zhou, 2019. "Boundary Value Problems for Hybrid Caputo Fractional Differential Equations," Mathematics, MDPI, vol. 7(3), pages 1-11, March.

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