Involvement of the fixed point technique for solving a fractional differential system

Abstract

Some physical phenomena were described through fractional differential equations and compared with integer-order differential equations which have better results, which is why researchers of different areas have paid great attention to study this direction. So, in this manuscript, we discuss the existence and uniqueness of solutions to a system of fractional deferential equations (FDEs) under Riemann-Liouville (R-L) integral boundary conditions. The solution method is obtained by two basic rules, the first rule is the Leray-Schauder alternative and the second is the Banach contraction principle. Finally, the theoretical results are supported by an illustrative example.

Keywords

• caputo fractional derivatives
• r-l integrals
• fixed point methodology
• leray-schauder alternative