Existence and Uniqueness of Solutions for the Nonlinear Fractional Differential Equations with Two-point and Integral Boundary Conditions
Keywords:Nonlocal boundary conditions, Caputo fractional derivative, existence, uniqueness, fixed point.
AbstractIn this paper the existence and uniqueness of solutions to the fractional differential equations with two-point and integral boundary conditions is investigated. The Green function is constructed, and the problem under consideration is reduced to the equivalent integral equation. Existence and uniqueness of a solution to this problem is analyzed using the Banach the contraction mapping principle and Krasnoselskiiâ€™s fixed point theorem.
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