Katugampola Fractional Differential Equation with Erdelyi-Kober Integral Boundary Conditions

Abstract

This paper investigates the following Katugampola fractional dierential equation with Erdelyi-Kober fractional integral boundary conditions:where D ρ,α is the Katugampola derivative of order 1 < α < 2, ρ > 0 and h : [0, T ] × R → R is a continuous function, I γ,δ η denotes Erdelyi-Kober fractional integral of order δ > 0, η > 0, λ, γ ∈ R. Some new existence and uniqueness results are obtained using nonlinear's contraction principal and Krasnoselskii's and Leray-Schauder's xed point theorems. Four examples are given in the last section to illustrate the obtained results.

Some Generalized Special Functions and their Properties

“…Qi and Wang [40] worked on Young's integral Inequalities and discussed its geometric interpretation. Adjimi and Benbachir [41] worked on Katugampola fractional dierential equation with Erdelyi-Kober integral boundary conditions. Furthermore, Mubeen and Iqbal [16] investigated the generalized version of Grüss-type inequalities by considering k-fractional integrals.…”