<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper, we establish sufficient conditions for the existence and stability of solutions for a class of boundary value problem for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle. Two examples are included to show the applicability of our results. </p></abstract>

In this paper, we establish sufficient conditions for the existence and stability of solutions for a class of boundary value problem for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle. Two examples are included to show the applicability of our results.

Existence and Stability Results for Nonlinear Boundary Value Problem for Implicit Differential Equations of Fractional Order

Laboratory of Mathematics, University of Sidi Bel-Abbes, P.O. Box 89 Sidi Bel Abbes 22000, Algeria

Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589,

Laboratory of Mathematics, University of Sidi Bel-Abbes, P.O. Box 89 Sidi Bel Abbes 22000,

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 establish sufficient conditions for the existence and stability of solutions for a class of boundary value problem for implicit fractional...

Existence and Stability Results for Nonlinear Boundary Value Problem for Implicit Differential Equations of Fractional Order

Article Category: Research Article

Published Online: Feb 04, 2017

Page range: 22 - 37

Received: Jan 08, 2015

Accepted: Jun 25, 2015

DOI: https://doi.org/10.7603/s40956-015-0002-9

Keywords
Boundary value conditions, Caputo’s fractional derivative, implicit fractional differential equations, fractional integral, existence, stability, fixed point

© 2017

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

Existence and Stability Results for Nonlinear Boundary Value Problem for Implicit Differential Equations of Fractional Order

Article Category: Research Article

Published Online: Feb 04, 2017

Page range: 22 - 37

Received: Jan 08, 2015

Accepted: Jun 25, 2015

DOI: https://doi.org/10.7603/s40956-015-0002-9

KeywordsBoundary value conditions, Caputo’s fractional derivative, implicit fractional differential equations, fractional integral, existence, stability, fixed point

© 2017

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

Keywords
Boundary value conditions, Caputo’s fractional derivative, implicit fractional differential equations, fractional integral, existence, stability, fixed point