Publication Date:
2015-10-16

Description:
We investigate sufficient conditions for existence and uniqueness of solutions for a coupled system of fractional order hybrid differential equations (HDEs) with multi-point hybrid boundary conditions given byD ω ( x ( t ) H ( t , x ( t ) , z ( t ) ) ) = − K 1 ( t , x ( t ) , z ( t ) ) , ω ∈ ( 2 , 3 ] , D ϵ ( z ( t ) G ( t , x ( t ) , z ( t ) ) ) = − K 2 ( t , x ( t ) , z ( t ) ) , ϵ ∈ ( 2 , 3 ] , x ( t ) H ( t , x ( t ) , z ( t ) ) | t = 1 = 0 , D μ ( x ( t ) H ( t , x ( t ) , z ( t ) ) ) | t = δ 1 = 0 , x ( 2 ) ( 0 ) = 0 , z ( t ) G ( t , x ( t ) , z ( t ) ) | t = 1 = 0 , D ν ( z ( t ) G ( t , x ( t ) , z ( t ) ) ) | t = δ 2 = 0 , z ( 2 ) ( 0 ) = 0 ,where t ∈ [ 0 , 1 ] , δ 1 , δ 2 , μ , ν ∈ ( 0 , 1 ) , and D ω , D ϵ , D μ and D ν are Caputo’s fractional derivatives of order ω, ϵ, μ and ν, respectively, K 1 , K 2 ∈ C ( [ 0 , 1 ] × R × R , R ) and G , H ∈ C ( [ 0 , 1 ] × R × R , R − { 0 } ) . We use classical results due to Dhage and Banach’s contraction principle (BCP) for the existence and uniqueness of solutions. For applications of our results, we include examples.

Print ISSN:
1687-1839

Electronic ISSN:
1687-1847

Topics:
Mathematics

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