Existence and Uniqueness of Solutions for Fractional Integro-Differential Equations Involving the Hadamard Derivatives
Existence and Uniqueness of Solutions for Fractional Integro-Differential Equations Involving the Hadamard Derivatives
In this paper, we study the existence and uniqueness of solutions for the following fractional boundary value problem, consisting of the Hadamard fractional derivative: HDαx(t)=Af(t,x(t))+∑i=1kCiHIβigi(t,x(t)),t∈(1,e), supplemented with fractional Hadamard boundary conditions: HDξx(1)=0,HDξx(e)=aHDα−ξ−12(HDξx(t))|t=δ,δ∈(1,e), where 1<α≤2, 0<ξ≤12, a∈(0,∞), 1<α−ξ<2, 0<βi<1, A,Ci, 1≤i≤k, are real constants, HDα is the Hadamard fractional derivative of …