Open AccessSome qualitative properties of nonlinear fractional integro-differential equations of variable order
Author(s) -
Ahmed Refice,
Mohammed Said Souid,
Ali Yakar
Publication year - 2021
Publication title -
an international journal of optimization and control: theories and applications/e-an international journal of optimization and control: theories and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.287
H-Index - 6
eISSN - 2146-5703
pISSN - 2146-0957
DOI - 10.11121/ijocta.2021.1198
Subject(s) - mathematics , uniqueness , piecewise , nonlinear system , mathematical analysis , fixed point theorem , variable (mathematics) , constant (computer programming) , stability (learning theory) , differential equation , fractional calculus , order (exchange) , computer science , physics , finance , quantum mechanics , machine learning , economics , programming language
The existence-uniqueness criteria of nonlinear fractional integro-differential equations of variable order with multiterm boundary value conditions are considered in this work. By utilizing the concepts of generalized intervals combined with the piecewise constant functions, we transform our problem into usual Caputo’s fractional differential equations of constant order. We develop the necessary criteria for assuring the solution's existence and uniqueness by applying Schauder and Banach fixed point theorem. We also examine the stability of the derived solution in the Ulam-Hyers-Rassias (UHR) sense and provide an example to demonstrate the credibility of the results.