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Solutions for a nonlinear fractional Euler–Lagrange type equation

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Abstract

The aim of this paper is the study of a nonlinear fractional Euler–Lagrange type equation with a nonlocal condition by means of lower and upper solutions method. For this purpose, we begin by solving an auxiliary problem by using Laplace transform, then we convert the posed problem to an equivalent right Caputo fractional differential equation with a vanishing terminal boundary condition. After constructing the lower and upper solutions, we define a sequence of modified problems that we solve by Schauder fixed point theorem. Finally, two numerical examples are given to illustrate the obtained results.

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Acknowledgements

The authors thank the anonymous referee for his valuable comments and suggestions that improved this paper.

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  1. Laboratory of Advanced Materials Department of Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, 23000, Annaba, Algeria

    A. Guezane-Lakoud & R Khaldi

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  1. A. Guezane-Lakoud
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  2. R Khaldi
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Correspondence to A. Guezane-Lakoud.

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Guezane-Lakoud, A., Khaldi, R. Solutions for a nonlinear fractional Euler–Lagrange type equation. SeMA 76, 195–202 (2019). https://doi.org/10.1007/s40324-018-0170-4

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  • DOI: https://doi.org/10.1007/s40324-018-0170-4

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