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Nonlinear Impulsive Multi-Order Caputo-Type Generalized Fractional Differential Equations with Infinite Delay

Author

Listed:
  • Bashir Ahmad

    (Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Madeaha Alghanmi

    (Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Ahmed Alsaedi

    (Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Ravi P. Agarwal

    (Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
    Department of Mathematics, Texas A&M University, Kingsville, TX 78363-8202, USA)

Abstract

We establish sufficient conditions for the existence of solutions for a nonlinear impulsive multi-order Caputo-type generalized fractional differential equation with infinite delay and nonlocal generalized integro-initial value conditions. The existence result is proved by means of Krasnoselskii’s fixed point theorem, while the contraction mapping principle is employed to obtain the uniqueness of solutions for the problem at hand. The paper concludes with illustrative examples.

Suggested Citation

  • Bashir Ahmad & Madeaha Alghanmi & Ahmed Alsaedi & Ravi P. Agarwal, 2019. "Nonlinear Impulsive Multi-Order Caputo-Type Generalized Fractional Differential Equations with Infinite Delay," Mathematics, MDPI, vol. 7(11), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1108-:d:287286
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    References listed on IDEAS

    as
    1. Ma, Jun & Xu, Ying & Wang, Chunni & Jin, Wuyin, 2016. "Pattern selection and self-organization induced by random boundary initial values in a neuronal network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 586-594.
    2. Rajavel, S. & Samidurai, R. & Cao, Jinde & Alsaedi, Ahmed & Ahmad, Bashir, 2017. "Finite-time non-fragile passivity control for neural networks with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 145-158.
    3. Xu, Wei & Zhu, Song & Fang, Xiaoyu & Wang, Wei, 2019. "Adaptive anti-synchronization of memristor-based complex-valued neural networks with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    4. Agarwal, Ravi & Hristova, S. & O’Regan, D., 2018. "Iterative techniques for the initial value problem for Caputo fractional differential equations with non-instantaneous impulses," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 407-421.
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