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

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

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∈0,1,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...

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Main Author: Nadir Benkaci-Ali
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2020/2127071
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spelling doaj-e1dd24930695429c8c311fdbebf052202020-11-25T01:25:40ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092020-01-01202010.1155/2020/21270712127071Positive Solution for the Integral and Infinite Point Boundary Value Problem for Fractional-Order Differential Equation Involving a Generalized ϕ-Laplacian OperatorNadir Benkaci-Ali0Faculty of Sciences, University M’Hmed Bouguerra, Boumerdes, AlgeriaIn 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∈0,1,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.http://dx.doi.org/10.1155/2020/2127071
collection DOAJ
language English
format Article
sources DOAJ
author Nadir Benkaci-Ali
spellingShingle Nadir Benkaci-Ali
Positive Solution for the Integral and Infinite Point Boundary Value Problem for Fractional-Order Differential Equation Involving a Generalized ϕ-Laplacian Operator
Abstract and Applied Analysis
author_facet Nadir Benkaci-Ali
author_sort Nadir Benkaci-Ali
title Positive Solution for the Integral and Infinite Point Boundary Value Problem for Fractional-Order Differential Equation Involving a Generalized ϕ-Laplacian Operator
title_short Positive Solution for the Integral and Infinite Point Boundary Value Problem for Fractional-Order Differential Equation Involving a Generalized ϕ-Laplacian Operator
title_full Positive Solution for the Integral and Infinite Point Boundary Value Problem for Fractional-Order Differential Equation Involving a Generalized ϕ-Laplacian Operator
title_fullStr Positive Solution for the Integral and Infinite Point Boundary Value Problem for Fractional-Order Differential Equation Involving a Generalized ϕ-Laplacian Operator
title_full_unstemmed Positive Solution for the Integral and Infinite Point Boundary Value Problem for Fractional-Order Differential Equation Involving a Generalized ϕ-Laplacian Operator
title_sort positive solution for the integral and infinite point boundary value problem for fractional-order differential equation involving a generalized ϕ-laplacian operator
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2020-01-01
description 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∈0,1,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.
url http://dx.doi.org/10.1155/2020/2127071
work_keys_str_mv AT nadirbenkaciali positivesolutionfortheintegralandinfinitepointboundaryvalueproblemforfractionalorderdifferentialequationinvolvingageneralizedphlaplacianoperator
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