Publication Date:
2015-05-09
Description:
In this paper, we investigate the existence and uniqueness of solutions to the coupled system of nonlinear fractional differential equations{ − D 0 + ν 1 y 1 ( t ) = λ 1 a 1 ( t ) f ( y 1 ( t ) , y 2 ( t ) ) , − D 0 + ν 2 y 2 ( t ) = λ 2 a 2 ( t ) g ( y 1 ( t ) , y 2 ( t ) ) ,where D 0 + ν is the standard Riemann-Liouville fractional derivative of order ν, t ∈ ( 0 , 1 ) , ν 1 , ν 2 ∈ ( n − 1 , n ] for n 〉 3 and n ∈ N , and λ 1 , λ 2 〉 0 , with the multi-point boundary value conditions: y 1 ( i ) ( 0 ) = 0 = y 2 ( i ) ( 0 ) , 0 ≤ i ≤ n − 2 ; D 0 + β y 1 ( 1 ) = ∑ i = 1 m − 2 b i D 0 + β y 1 ( ξ i ) ; D 0 + β y 2 ( 1 ) = ∑ i = 1 m − 2 b i D 0 + β y 2 ( ξ i ) , where n − 2 〈 β 〈 n − 1 , 0 〈 ξ 1 〈 ξ 2 〈 ⋯ 〈 ξ m − 2 〈 1 , b i ≥ 0 ( i = 1 , 2 , … , m − 2 ) with ρ 1 : = ∑ i = 1 m − 2 b i ξ i ν 1 − β − 1 〈 1 , and ρ 2 : = ∑ i = 1 m − 2 b i ξ i ν 2 − β − 1 〈 1 . Our analysis relies on the Banach contraction principle and Krasnoselskii’s fixed point theorem.MSC: 26A33, 34B18, 34B27.
Print ISSN:
1687-1839
Electronic ISSN:
1687-1847
Topics:
Mathematics
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