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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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2020/2127071 |
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| author | Nadir Benkaci-Ali |
| author_facet | Nadir Benkaci-Ali |
| author_sort | Nadir Benkaci-Ali |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-e1dd24930695429c8c311fdbebf05220 |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e1dd24930695429c8c311fdbebf052202025-08-20T03:20:59ZengWileyAbstract 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2020/2127071 |
| work_keys_str_mv | AT nadirbenkaciali positivesolutionfortheintegralandinfinitepointboundaryvalueproblemforfractionalorderdifferentialequationinvolvingageneralizedphlaplacianoperator |