A study on Hilfer–Katugampola fractional differential equations with boundary conditions

Abstract

Abstract In this paper, we investigate the existence of solutions of Hilfer-Katugampola fractional differential equations with boundary conditions. We first establish existence theory of solutions for the mentioned problem by the fixed point theory and the measure of noncompactness. Then we investigate the ε-approximate solution to our concerned problem via a generalized Gronwall inequality. Finally, as the application of abstract results, we give an example to illustrate our main results.

Keywords

• Hilfer–Katugampola fractional derivative
• Boundary conditions
• Mönch fixed point
• Measure of noncompactness
• ε-approximate