Existence results for the σ-Hilfer hybrid fractional boundary value problem involving a weighted φ-Laplacian operator

Abstract

. In this paper, we are interested in the existence of positive solutions for the Hilfer hybrid fractional equation involving a weighted two dimensional φ -Laplacian operator with the integral-in fi nite point boundary conditions. In this approach, we transform the given fractional differential equation into an equivalent integral equation. Then we establish suf fi cient conditions and employ the fi xed point index arguments to obtain new results on the existence of positive solutions. Examples illustrating the main results are also constructed. This work contains several new ideas, and gives a uni fi ed approach applicable to many boundary value problems involving ( p , q ) -Laplacian type operators.