<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper we are concerned with nonlinear implicit fractional differential equations with initial conditions. We prove the existence and uniqueness results by using modified version of contraction principle. Further, our prime aim is to present various Ulam-Hyers stability and E<sub>α</sub>-Ulam-Hyers stability results via successive approximation method. </p></abstract>

In this paper we are concerned with nonlinear implicit fractional differential equations with initial conditions. We prove the existence and uniqueness results by using modified version of contraction principle. Further, our prime aim is to present various Ulam-Hyers stability and Eα-Ulam-Hyers stability results via successive approximation method.

Stability via successive approximation for nonlinear implicit fractional differential equations

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

In this paper we are concerned with nonlinear implicit fractional differential equations with initial conditions. We prove the existence and uniqueness results...

Stability via successive approximation for nonlinear implicit fractional differential equations

Published Online: Aug 01, 2017

Page range: 36 - 54

Received: Jun 08, 2016

Accepted: Nov 24, 2016

DOI: https://doi.org/10.1515/mjpaa-2017-0004

Keywords
Implicit fractional differential equation, Modified version of contraction principle, Existence, Ulam-Hyers Stability, Successive approximations

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Stability via successive approximation for nonlinear implicit fractional differential equations

Published Online: Aug 01, 2017

Page range: 36 - 54

Received: Jun 08, 2016

Accepted: Nov 24, 2016

DOI: https://doi.org/10.1515/mjpaa-2017-0004

KeywordsImplicit fractional differential equation, Modified version of contraction principle, Existence, Ulam-Hyers Stability, Successive approximations

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Implicit fractional differential equation, Modified version of contraction principle, Existence, Ulam-Hyers Stability, Successive approximations