Uniqueness and Asymptotic Behavior of Positive Solutions for a Fractional-Order Integral Boundary Value Problem
We study a model arising from porous media, electromagnetic, and signal processing of wireless communication system -𝒟tαx(t)=f(t,x(t),x'(t),x”(t),…,x(n-2)(t)), 0<t<1, x(0)=x'(0)=⋯=x(n-2)(0)=0, x(n-2)(1)=∫01x(n-2)(s)dA(s), where...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/294694 |
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| author | Min Jia Xin Liu Xuemai Gu |
| author_facet | Min Jia Xin Liu Xuemai Gu |
| author_sort | Min Jia |
| collection | DOAJ |
| description | We study a model arising from porous media, electromagnetic, and signal processing of wireless communication system
-𝒟tαx(t)=f(t,x(t),x'(t),x”(t),…,x(n-2)(t)), 0<t<1,
x(0)=x'(0)=⋯=x(n-2)(0)=0,
x(n-2)(1)=∫01x(n-2)(s)dA(s), where n-1<α≤n,
n∈ℕ and n≥2, 𝒟tα is the standard Riemann-Liouville derivative, ∫01x(s)dA(s) is linear functionals given by Riemann-Stieltjes integrals, A is a function of bounded variation, and dA can be a changing-sign measure. The existence, uniqueness, and asymptotic behavior of positive solutions to the singular nonlocal integral boundary value problem for fractional differential equation are obtained. Our analysis relies on Schauder's fixed-point theorem and upper and lower solution method. |
| format | Article |
| id | doaj-art-d8e840165b5f4912bbee12cb571a7d6d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d8e840165b5f4912bbee12cb571a7d6d2025-02-03T01:11:42ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/294694294694Uniqueness and Asymptotic Behavior of Positive Solutions for a Fractional-Order Integral Boundary Value ProblemMin Jia0Xin Liu1Xuemai Gu2Communication Research Center, Harbin Institute of Technology, Harbin 150080, ChinaCommunication Research Center, Harbin Institute of Technology, Harbin 150080, ChinaCommunication Research Center, Harbin Institute of Technology, Harbin 150080, ChinaWe study a model arising from porous media, electromagnetic, and signal processing of wireless communication system -𝒟tαx(t)=f(t,x(t),x'(t),x”(t),…,x(n-2)(t)), 0<t<1, x(0)=x'(0)=⋯=x(n-2)(0)=0, x(n-2)(1)=∫01x(n-2)(s)dA(s), where n-1<α≤n, n∈ℕ and n≥2, 𝒟tα is the standard Riemann-Liouville derivative, ∫01x(s)dA(s) is linear functionals given by Riemann-Stieltjes integrals, A is a function of bounded variation, and dA can be a changing-sign measure. The existence, uniqueness, and asymptotic behavior of positive solutions to the singular nonlocal integral boundary value problem for fractional differential equation are obtained. Our analysis relies on Schauder's fixed-point theorem and upper and lower solution method.http://dx.doi.org/10.1155/2012/294694 |
| spellingShingle | Min Jia Xin Liu Xuemai Gu Uniqueness and Asymptotic Behavior of Positive Solutions for a Fractional-Order Integral Boundary Value Problem Abstract and Applied Analysis |
| title | Uniqueness and Asymptotic Behavior of Positive Solutions for a Fractional-Order Integral Boundary Value Problem |
| title_full | Uniqueness and Asymptotic Behavior of Positive Solutions for a Fractional-Order Integral Boundary Value Problem |
| title_fullStr | Uniqueness and Asymptotic Behavior of Positive Solutions for a Fractional-Order Integral Boundary Value Problem |
| title_full_unstemmed | Uniqueness and Asymptotic Behavior of Positive Solutions for a Fractional-Order Integral Boundary Value Problem |
| title_short | Uniqueness and Asymptotic Behavior of Positive Solutions for a Fractional-Order Integral Boundary Value Problem |
| title_sort | uniqueness and asymptotic behavior of positive solutions for a fractional order integral boundary value problem |
| url | http://dx.doi.org/10.1155/2012/294694 |
| work_keys_str_mv | AT minjia uniquenessandasymptoticbehaviorofpositivesolutionsforafractionalorderintegralboundaryvalueproblem AT xinliu uniquenessandasymptoticbehaviorofpositivesolutionsforafractionalorderintegralboundaryvalueproblem AT xuemaigu uniquenessandasymptoticbehaviorofpositivesolutionsforafractionalorderintegralboundaryvalueproblem |