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

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