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Analysis of Stochastic Weighted Impulsive Neutral ψ-Hilfer Integro-Fractional Differential System with Delay

Author

Listed:
  • Manzoor Ahmad
  • Akbar Zada
  • Jihad Ahmad
  • Mohamed A. Abd El Salam
  • Ali Ahmadian

Abstract

This paper is devoted to the study of stochastic fractional differential equations. Particularly, we study the existence and uniqueness of solutions of nonlinear stochastic weighted impulsive ψ-Hilfer neutral integro-fractional differential system with infinite delay. We obtain the results with the help of fixed-point theorems and Banach contraction principle. Additionally, we investigate the Ulam–Hyers stability of the solutions using basic schemes of fractional calculus. For application of the theory, we add an example.

Suggested Citation

  • Manzoor Ahmad & Akbar Zada & Jihad Ahmad & Mohamed A. Abd El Salam & Ali Ahmadian, 2022. "Analysis of Stochastic Weighted Impulsive Neutral ψ-Hilfer Integro-Fractional Differential System with Delay," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-23, March.
    • Handle: RePEc:hin:jnlmpe:1490583
    DOI: 10.1155/2022/1490583
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    Cited by:

    1. Rhaima, Mohamed & Mchiri, Lassaad & Ben Makhlouf, Abdellatif & Ahmed, Hassen, 2024. "Ulam type stability for mixed Hadamard and Riemann–Liouville Fractional Stochastic Differential Equations," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Kuang, Daipeng & Li, Jianli & Gao, Dongdong & Luo, Danfeng, 2024. "Stochastic near-optimal control for a system with Markovian switching and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    3. Hamza Khalil & Akbar Zada & Mohamed Rhaima & Ioan-Lucian Popa, 2024. "Analysis of Neutral Implicit Stochastic Hilfer Fractional Differential Equation Involving Lévy Noise with Retarded and Advanced Arguments," Mathematics, MDPI, vol. 12(21), pages 1-15, October.

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