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Positive Solution for the Integral and Infinite Point Boundary Value Problem for Fractional‐Order Differential Equation Involving a Generalized ϕ‐Laplacian Operator

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  • Nadir Benkaci-Ali

Abstract

In this paper, we establish the existence of nontrivial positive solution to the following integral‐infinite point boundary‐value problem involving ϕ‐Laplacian operator D0+αϕx,D0+βux+fx,ux=0,x∈01,,D0+σu0=D0+βu0=0,u1=∫01 gtutdt+∑n=1n=+∞ αnuηn, where ϕ : [0, 1] × R → R is a continuous function and D0+p is the Riemann‐Liouville derivative for p ∈ {α, β, σ}. By using some properties of fixed point index, we obtain the existence results and give an example at last.

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Handle: RePEc:wly:jnlaaa:v:2020:y:2020:i:1:n:2127071
DOI: 10.1155/2020/2127071
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