<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this manuscript, we study the existence, uniqueness and various kinds of Ulam stability including Ulam–Hyers stability, generalized Ulam– Hyers stability, Ulam–Hyers–Rassias stability, and generalized Ulam–Hyers– Rassias stability of the solution to an implicit nonlinear fractional differential equations corresponding to an implicit integral boundary condition. We develop conditions for the existence and uniqueness by using the classical fixed point theorems such as Banach contraction principle and Schaefer’s fixed point theorem. For stability, we utilize classical functional analysis. The main results are well illustrated with an example.</p></abstract>

In this manuscript, we study the existence, uniqueness and various kinds of Ulam stability including Ulam–Hyers stability, generalized Ulam– Hyers stability, Ulam–Hyers–Rassias stability, and generalized Ulam–Hyers– Rassias stability of the solution to an implicit nonlinear fractional differential equations corresponding to an implicit integral boundary condition. We develop conditions for the existence and uniqueness by using the classical fixed point theorems such as Banach contraction principle and Schaefer’s fixed point theorem. For stability, we utilize classical functional analysis. The main results are well illustrated with an example.

Stability analysis of implicit fractional differential equation with anti–periodic integral boundary value problem

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

In this manuscript, we study the existence, uniqueness and various kinds of Ulam stability including Ulam–Hyers stability, generalized Ulam– Hyers stability,...

Stability analysis of implicit fractional differential equation with anti–periodic integral boundary value problem

Published Online: Dec 31, 2020

Page range: 5 - 25

Received: Jan 21, 2019

Accepted: Jul 18, 2019

DOI: https://doi.org/10.2478/aupcsm-2020-0001

Keywords
Implicit fractional differential equations, Fixed point theorem, Hyers–Ulam Stability

© 2020 Akbar Zada et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Stability analysis of implicit fractional differential equation with anti–periodic integral boundary value problem

Published Online: Dec 31, 2020

Page range: 5 - 25

Received: Jan 21, 2019

Accepted: Jul 18, 2019

DOI: https://doi.org/10.2478/aupcsm-2020-0001

KeywordsImplicit fractional differential equations, Fixed point theorem, Hyers–Ulam Stability

© 2020 Akbar Zada et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Keywords
Implicit fractional differential equations, Fixed point theorem, Hyers–Ulam Stability