الفهرس | Only 14 pages are availabe for public view |
Abstract In this work we are concerned with the existence of a unique solution of some nonlocal, two point, problem of functional integro-differential equation with arbitrary (fractional) orders. Firstly, in Chapter 2, we are concerned by with the nonlocal (two point) problem of integro-differential equation of arbitrary (fractional) orders dx Z 1 = f (t, dt 0 k(t, s)Dα x(s)ds), t ∈ (0, 1) with the nonlocal condition x(τ ) = γ x(ξ), τ ∈ [0, 1) , ξ ∈ (0, 1] , γ = 1. The existence of a unique solution x ∈ C[0, 1] and dx ∈ C[0, 1] will be proved. Also the existence of a unique absolutely continuous solution , x ∈ AC[0, 1] will be also proved. Also in L1[0, 1]. Secondly, in Chapter 3, we study the nonlocal (two point) problem of the integro-functional differential equations dx Z 1 = f (t, dt 0 k(t, s)g(s, Dα x(s)ds)), t ∈ (0, 1) with the nonlocal condition x(τ ) = γ x(ξ), τ ∈ [0, 1) , ξ ∈ (0, 1] , γ = 1. The existence of a unique solution x ∈ C[0, 1] and dx ∈ C[0, 1] will be proved. Also the existence of a unique absolutely continuous solution , x ∈ AC[0, 1] will be also proved. Also in L1[0, 1]. |