Existence of Solution for a Katugampola Fractional Differential Equation Using Coincidence Degree Theory

In this paper, the authors study the existence of positive solutions to the fractional boundary value problem at resonance (Formula presented.) where 1<α≤2, and D_a+^α,ρ is a Katugampola fractional derivative, which generalizes the Riemann–Liouville and Hadamard fractional derivatives, and ∫_a^bx(t)dA(t) denotes a Riemann–Stieltjes integral of x with respect to A, where A is a function of bounded variation. Coincidence degree theory is applied to obtain existence results. This appears to be the first work in the literature to deal with a resonant fractional differential equation with a Katugampola fractional derivative. Examples are given to illustrate the application of their results.