Hilfer-Katugampola fractional stochastic differential equations with nonlocal conditions

Sayed Ahmed, A.M.; M. Ahmed, Hamdy

doi:10.22075/ijnaa.2022.27337.3562

Hilfer-Katugampola fractional stochastic differential equations with nonlocal conditions

Document Type : Research Paper

Authors

A.M. Sayed Ahmed ¹

Hamdy M. Ahmed ²

¹ Department of Mathematics and Computer Science, Faculty of Sciences, Alexandria University, Alexandria, Egypt

² Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El-Shorouk Academy, El-Shorouk City, Cairo, Egypt

10.22075/ijnaa.2022.27337.3562

Abstract

Hilfer-Katugampola-type fractional stochastic differential equations with nonlocal conditions are considered in this paper. By using the fixed point theorem, the existence and uniqueness of solutions for the considered problem are proved. Ulam-Hyers stability for the considered problem is studied. Finally, an example is presented to show our main results.

Keywords

Hilfer-Katugampola fractional derivative

Stochastic differential equation

Ulam-Hyers stability

fixed point theorem

Nonlocal conditions