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On new approach of fractional derivative by Mittag-Leffler kernel to neutral integro-differential systems with impulsive conditions

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  • Ravichandran, C.
  • Logeswari, K.
  • Panda, Sumati Kumari
  • Nisar, Kottakkaran Sooppy

Abstract

In this article, we study an impulsive neutral fractional integro-differential equation (FIDE) via Atangana-Baleanu fractional derivative. The fixed point approach is employed to prove the existence results of the equation with initial and non-local conditions. The application of the results obtained are verified using suitable examples of different fractional orders.

Suggested Citation

  • Ravichandran, C. & Logeswari, K. & Panda, Sumati Kumari & Nisar, Kottakkaran Sooppy, 2020. "On new approach of fractional derivative by Mittag-Leffler kernel to neutral integro-differential systems with impulsive conditions," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304100
    DOI: 10.1016/j.chaos.2020.110012
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    5. Panda, Sumati Kumari & Nagy, A.M. & Vijayakumar, Velusamy & Hazarika, Bipan, 2023. "Stability analysis for complex-valued neural networks with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    6. Muñoz-Vázquez, Aldo Jonathan & Martínez-Fuentes, Oscar & Fernández-Anaya, Guillermo, 2022. "Generalized PI control for robust stabilization of dynamical systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 22-35.
    7. Xin Liu & Lili Chen & Yanfeng Zhao, 2023. "Existence Theoremsfor Solutions of a Nonlinear Fractional-Order Coupled Delayed System via Fixed Point Theory," Mathematics, MDPI, vol. 11(7), pages 1-15, March.
    8. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Shukla, Anurag & Nisar, Kottakkaran Sooppy, 2021. "A note on approximate controllability for nonlocal fractional evolution stochastic integrodifferential inclusions of order r∈(1,2) with delay," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    9. Nisar, Kottakkaran Sooppy & Logeswari, K. & Ravichandran, C. & Sabarinathan, S., 2023. "New frame of fractional neutral ABC-derivative with IBC and mixed delay," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
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