ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Local Existence and Ulam Stability Results for Nonlinear Fractional Differential Equations

Journal of Applied Nonlinear Dynamics 9(4) (2020) 655--666 | DOI:10.5890/JAND.2020.12.009

Houssem Eddine Khochemane$^{1}$, Abdelouaheb Ardjouni$^{2}$ , Amin Guerouah$^{3}$, Salah Zitouni$^{2}$

$^1$ Ecole normale sup'{e}rieure d'enseignement technologique, Azzaba-Skikda, Algeria

$^2$ Department of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, Souk Ahras, 41000, Algeria

$^3$ Mustapha Ben Boulaid University, Batna 2-fesdis, 05001 Batna, Algeria

Abstract

The aim of this paper is to study the existence and uniqueness for nonlinear fractional differential equations involving Caputo's fractional derivative using the Krasnoselskii and Banach fixed point theorems on one hand and to establish the Ulam stability on the other hand. Finally, An example is given to substantiate the usefulness of the obtained results.

Acknowledgments

\bibitem {4}Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J. (2006), \textit{Theory and applications of fractional differential equations}, Amsterdam, the Netherlands, North-Holland.

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