Existence of solutions to the iterative system of nonlinear two-point tempered fractional order boundary value problems

Mahammad Khuddush

In this paper we study the iterative system of nonlinear two-point tempered fractional order boundary value problems. By means of Krasnoselskii's fixed point theorem on cone, some existence results of positive solutions are obtained. The proofs are based upon the reduction of problem considered to the equivalent Fredholm integral equation of second kind. Further, we study the existence of unique solution by an application of Rus's theorem and Hyers-Ulam stability of the adderessed problem for l=1. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 16(2) (2023), pp. 97-114