Nonlocal Impulsive Fractional Integral Boundary Value Problem for (ρk,ϕk)-Hilfer Fractional Integro-Differential Equations

Marisa Kaewsuwan, Rachanee Phuwapathanapun, Weerawat Sudsutad, Jehad Alzabut, Chatthai Thaiprayoon, Jutarat Kongson
2022 Mathematics  
In this paper, we establish the existence and stability results for the (ρk,ϕk)-Hilfer fractional integro-differential equations under instantaneous impulse with non-local multi-point fractional integral boundary conditions. We achieve the formulation of the solution to the (ρk,ϕk)-Hilfer fractional differential equation with constant coefficients in term of the Mittag–Leffler kernel. The uniqueness result is proved by applying Banach's fixed point theory with the Mittag–Leffler properties, and
more » ... the existence result is derived by using a fixed point theorem due to O'Regan. Furthermore, Ulam–Hyers stability and Ulam–Hyers–Rassias stability results are demonstrated via the non-linear functional analysis method. In addition, numerical examples are designed to demonstrate the application of the main results.
doi:10.3390/math10203874 fatcat:caza5vrxynd5jkk2voxborenhe