Analysis of some Katugampola fractional differential equations with fractional boundary conditions

Abstract

In this work, some class of the fractional differential equations under fractional boundary conditions with the Katugampola derivative is considered. By proving the Lyapunov-type inequality, there are deduced the conditions for existence, and non-existence of the solutions to the considered boundary problem. Moreover, we present some examples to demonstrate the effectiveness and applications of the new results.

Keywords

• fractional calculus
• lyapunov inequality
• green function
• fractional differential equations
• katugampola derivative
• eigenvalue of fractional differential equation