Fractional neutral stochastic integrodifferential equations with Caputo fractional derivative

Rosenblatt process, Poisson jumps and Optimal control

Authors

  • K. Ravikumar PSG College of Arts and Science.
  • K. Ramkumar PSG College of Arts and Science.
  • Hamdy Ahmed El-Shorouk Academy.

DOI:

https://doi.org/10.22199/issn.0717-6279-4329

Keywords:

fractional neutral stochastic integrodifferential system, Rosenblatt process, Poisson jumps, optimal control, successive approximation

Abstract

The objective of this paper is to investigate the existence of mild solutions and optimal controls for a class of fractional neutral stochastic integrodifferential equations driven by Rosenblatt process and Poisson jumps in Hilbert spaces. First we establish a new set of sufficient conditions for the existence of mild solutions of the aforementioned fractional systems by using the successive approximation approach.

The results are formulated and proved by using the fractional calculus, solution operator and stochastic analysis techniques. The existence of optimal control pairs of system governed by fractional neutral stochastic differential equations driven by Rosenblatt process and poisson jumps is also been presented. An example is provided to illustrate the theory.

Author Biographies

K. Ravikumar, PSG College of Arts and Science.

Department of Mathematics.

K. Ramkumar, PSG College of Arts and Science.

Department of Mathematics.

Hamdy Ahmed, El-Shorouk Academy.

Higher Institute of Engineering.

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Published

2023-05-09

How to Cite

[1]
K. . Ravikumar, K. . Ramkumar, and H. Ahmed, “ Fractional neutral stochastic integrodifferential equations with Caputo fractional derivative: Rosenblatt process, Poisson jumps and Optimal control”, Proyecciones (Antofagasta, On line), vol. 42, no. 3, pp. 549-570, May 2023.

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