On the existence of solutions for a multi-singular pointwise defined fractional system

Abstract

Abstract One of best ways for increasing our abilities in exact modeling of natural phenomena is working with a singular version of different fractional differential equations. As is well known, multi-singular equations are a modern version of singular equations. In this paper, we investigate the existence of solutions for a multi-singular fractional differential system. We consider some particular boundary value conditions on the system. By using the α-ψ-contractions and locating some control conditions, we prove that the system via infinite singular points has solutions. Finally, we provide an example to illustrate our main result.

Keywords

• Boundary value condition
• Multi-singular system
• Solution of a pointwise defined equation
• The fractional Caputo derivative