Neutral delay Hilfer fractional integrodifferential equations with fractional brownian motion

Yousef Alnafisah; Hamdy M. Ahmed

doi:10.3934/eect.2021031

Article Contents

2022, Volume 11, Issue 3: 925-937. Doi: 10.3934/eect.2021031

This issue Previous Article Long-time behavior of a size-structured population model with diffusion and delayed birth process Next Article Local stabilization of viscous Burgers equation with memory

Neutral delay Hilfer fractional integrodifferential equations with fractional brownian motion

Yousef Alnafisah^1, and
Hamdy M. Ahmed^2,

1.
Mathematics Department, College of Science, Qassim University, P.O.Box 6644, Buraydah 51452, Saudi Arabia
2.
Higher Institute of Engineering, El-Shorouk Academy, El-Shorouk City, Cairo, Egypt

^* Corresponding author: Hamdy M. Ahmed
^* Corresponding author: Hamdy M. Ahmed

Received: May 31, 2020

Revised: April 30, 2021

Published: June 2022

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Abstract

In this paper, we study the existence and uniqueness of mild solutions for neutral delay Hilfer fractional integrodifferential equations with fractional Brownian motion. Sufficient conditions for controllability of neutral delay Hilfer fractional differential equations with fractional Brownian motion are established. The required results are obtained based on the fixed point theorem combined with the semigroup theory, fractional calculus and stochastic analysis. Finally, an example is given to illustrate the obtained results.

Keywords:

Neutral delay integrodifferential equations,
Hilfer fractional derivative,
Existence of solutions,
controllability.

Mathematics Subject Classification: 93B05; 34A08; 60G51.

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References

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