Unique Solution for Multi-point Fractional Integro-Differential Equations

Chengbo Zhai 1  and Lifang Wei 2
  • 1 School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, P.R. China
  • 2 School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, P.R. China
Chengbo Zhai
  • Corresponding author
  • School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, P.R. China
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and Lifang Wei

Abstract

We study a fractional integro-differential equation subject to multi-point boundary conditions:

D0+αu(t)+f(t,u(t),Tu(t),Su(t))=b, t(0,1),u(0)=u(0)==u(n2)(0)=0,D0+pu(t)|t=1=i=1maiD0+qu(t)|t=ξi,

where α(n1,n], nN, n3, ai0, 0<ξ1<<ξm1, p[1,n2], q[0,p],b>0. By utilizing a new fixed point theorem of increasing ψ(h,r) concave operators defined on special sets in ordered spaces, we demonstrate existence and uniqueness of solutions for this problem. Besides, it is shown that an iterative sequence can be constructed to approximate the unique solution. Finally, the main result is illustrated with the aid of an example.

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