Abstract and Applied Analysis

The Existence of Positive Solutions for a New Coupled System of Multiterm Singular Fractional Integrodifferential Boundary Value Problems

Dumitru Baleanu, Sayyedeh Zahra Nazemi, and Shahram Rezapour

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Abstract

We discuss the existence of positive solutions for the coupled system of multiterm singular fractional integrodifferential boundary value problems D 0 + α u ( t ) + f 1 ( t , u ( t ) , v ( t ) , ( ϕ 1 u ) ( t ) , ( ψ 1 v ) ( t ) , D 0 + p u ( t ) , D 0 + μ 1 v ( t ) , D 0 + μ 2 v ( t ) , , D 0 + μ m v ( t ) ) = 0 , D 0 + β v ( t ) + f 2 ( t , u ( t ) , v ( t ) , ( ϕ 2 u ) ( t ) , ( ψ 2 v ) ( t ) , D 0 + q v ( t ) , D 0 + ν 1 u ( t ) , D 0 + ν 2 u ( t ) , , D 0 + ν m u ( t ) ) = 0 , u ( i ) ( 0 ) = 0 and v ( i ) ( 0 ) = 0 for all 0 i n - 2 , [ D 0 + δ 1 u ( t ) ] t = 1 = 0 for 2 < δ 1 < n - 1 and α - δ 1 1 , [ D 0 + δ 2 v ( t ) ] t = 1 = 0 for 2 < δ 2 < n - 1 and β - δ 2 1 , where n 4 , n - 1 < α , β < n , 0 < p , q < 1 , 1 < μ i , ν i < 2   ( i = 1,2 , , m ) , γ j , λ j : [ 0,1 ] × [ 0,1 ] ( 0 , ) are continuous functions ( j = 1,2 ) and ( ϕ j u ) ( t ) = 0 t γ j ( t , s ) u ( s ) d s , ( ψ j v ) ( t ) = 0 t λ j ( t , s ) v ( s ) d s . Here D is the standard Riemann-Liouville fractional derivative, f j   ( j = 1,2 ) is a Caratheodory function, and f j ( t , x , y , z , w , v , u 1 , u 2 , , u m ) is singular at the value 0 of its variables.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 368659, 15 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393450382

Digital Object Identifier
doi:10.1155/2013/368659

Mathematical Reviews number (MathSciNet)
MR3132540

Zentralblatt MATH identifier
1294.45005

Citation

Baleanu, Dumitru; Nazemi, Sayyedeh Zahra; Rezapour, Shahram. The Existence of Positive Solutions for a New Coupled System of Multiterm Singular Fractional Integrodifferential Boundary Value Problems. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 368659, 15 pages. doi:10.1155/2013/368659. https://projecteuclid.org/euclid.aaa/1393450382


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