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The Existence of Solutions for a Nonlinear First-Order Differential Equation Involving the Riemann–Liouville Fractional-Order and Nonlocal Condition

  • Fatma M. Gaafar
Article

Abstract

In this paper, we study necessary conditions for the existence and uniqueness of continuous solution for a nonlocal boundary value problem with nonlinear term involving Riemann–Liouville fractional derivative. Our results are based on Schauder fixed point theorem and the Banach contraction principle fixed point theorem. Examples illustrating the obtained results are also presented.

Keywords

First-order differential equation Riemann–Liouville fractional derivative Boundary value problem Existence of solutions Nonlocal condition 

Mathematics Subject Classification

26A33 34B10 

Notes

Acknowledgements

The author wishes to express here thanks to the editor and the reviewers for a careful reading of this paper and the valuable comments and suggestions that led to the improvement of the original manuscript.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Beside Damanhour General HospitalDamanhourEgypt

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