'Vladikavkaz Scientific Centre of the Russian Academy of Sciences'
Doi
Abstract
Fractional calculus is considered to be a powerful tool in describing complex systems with
a wide range of applicability in many fields of science and engineering. The behavior of many systems can
be described by using fractional differential equations with boundary conditions. In this sense, the study
on the stability of fractional boundary value problems is of high importance.
The main goal of this paper is to investigate the Ulam–Hyers stability and Ulam–Hyers–Rassias stability
of a class of fractional four-point boundary value problem involving Caputo derivative and with a given
parameter. By using contraction principles, sufficient conditions are obtained to guarantee the uniqueness
of solution. Therefore, we obtain sufficient conditions for the stability of that class of nonlinear fractional
boundary value problems on the space of continuous functions. The presented results improve and extend
some previous research. Finally, we construct some examples to illustrate the theoretical results.This work is supported by the Center for Research and Development in Mathematics and Applications
(CIDMA) through the Portuguese Foundation for Science and Technology (FCT - Fundação para a Ciência
e a Tecnologia), reference UIDB/04106/2020. Additionally, A. Silva is also funded by national funds (OE),
through FCT, I.P., in the scope of the framework contract foreseen in the numbers 4, 5 and 6 of the article 23,
of the Decree-Law 57/2016, of August 29, changed by Law 57/2017, of July 19.publishe
