Existence and uniqueness for ψ‐Hilfer fractional differential equation with nonlocal multi‐point condition.

In this paper, we study and investigate the ψ−Hilfer fractional differential equation with nonlocal multi‐point condition of the form: Da+q,p;ψu(t)=f(t,u(t),Da+q,p;ψu(t)),t∈[a,b],Ia+1−r;ψu(a)=∑i=1mβiu(ηi),q≤r=q+p−qp<1,ηi∈[a,b], where 0<q<1,0≤p≤1,m∈N, βi∈R, i=1,2,...,m, −∞<a<b<∞, Da+q,p;ψ is the ψ− Hilfer fractional derivative, f:[a,b]×R×R→R is a continuous function, and Ia+1−r;ψ is the ψ‐Riemann‐Liouville fractional integral of order 1−r. By using Schaefer's and Banach fixed point theorems, we prove the existence, uniqueness, and stability analysis of this problem. An example is given to illustrate the applicability of our results. [ABSTRACT FROM AUTHOR]