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Keywords = (ρ,ϕ)-Hilfer fractional derivative

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40 pages, 783 KiB  
Article
Nonlocal Impulsive Fractional Integral Boundary Value Problem for (ρk,ϕk)-Hilfer Fractional Integro-Differential Equations
by Marisa Kaewsuwan, Rachanee Phuwapathanapun, Weerawat Sudsutad, Jehad Alzabut, Chatthai Thaiprayoon and Jutarat Kongson
Mathematics 2022, 10(20), 3874; https://doi.org/10.3390/math10203874 - 18 Oct 2022
Cited by 6 | Viewed by 1770
Abstract
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 [...] Read more.
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 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. Full article
(This article belongs to the Special Issue Fractional Differential Equations: Theory and Application)
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