Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations
We study some existence results in a Banach space for a nonlocal boundary value problem involving a nonlinear differential equation of fractional order q given by cDqx(t)=f(t,x(t)), 0<t<1, q∈(m−1,m], m∈ℕ, m≥2, x(0)=0, x′(0)=0, x′′(0)=0,…,x(m−2)(0)=0, x(1)=αx(η). Our results are based on the co...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2009/494720 |
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| _version_ | 1849410900959690752 |
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| author | Bashir Ahmad Juan J. Nieto |
| author_facet | Bashir Ahmad Juan J. Nieto |
| author_sort | Bashir Ahmad |
| collection | DOAJ |
| description | We study some existence results in a Banach space for a
nonlocal boundary value problem involving a nonlinear differential equation
of fractional order q given by cDqx(t)=f(t,x(t)), 0<t<1, q∈(m−1,m], m∈ℕ, m≥2, x(0)=0, x′(0)=0, x′′(0)=0,…,x(m−2)(0)=0, x(1)=αx(η). Our results are based on the contraction mapping principle and Krasnoselskii's fixed point theorem. |
| format | Article |
| id | doaj-art-5abb51fa278b411f9d82c4d90942ebfa |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5abb51fa278b411f9d82c4d90942ebfa2025-08-20T03:34:57ZengWileyAbstract and Applied Analysis1085-33751687-04092009-01-01200910.1155/2009/494720494720Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential EquationsBashir Ahmad0Juan J. Nieto1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782 Santiago de Compostela, SpainWe study some existence results in a Banach space for a nonlocal boundary value problem involving a nonlinear differential equation of fractional order q given by cDqx(t)=f(t,x(t)), 0<t<1, q∈(m−1,m], m∈ℕ, m≥2, x(0)=0, x′(0)=0, x′′(0)=0,…,x(m−2)(0)=0, x(1)=αx(η). Our results are based on the contraction mapping principle and Krasnoselskii's fixed point theorem.http://dx.doi.org/10.1155/2009/494720 |
| spellingShingle | Bashir Ahmad Juan J. Nieto Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations Abstract and Applied Analysis |
| title | Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations |
| title_full | Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations |
| title_fullStr | Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations |
| title_full_unstemmed | Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations |
| title_short | Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations |
| title_sort | existence of solutions for nonlocal boundary value problems of higher order nonlinear fractional differential equations |
| url | http://dx.doi.org/10.1155/2009/494720 |
| work_keys_str_mv | AT bashirahmad existenceofsolutionsfornonlocalboundaryvalueproblemsofhigherordernonlinearfractionaldifferentialequations AT juanjnieto existenceofsolutionsfornonlocalboundaryvalueproblemsofhigherordernonlinearfractionaldifferentialequations |