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On a fractional boundary value problem in a weighted space

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Abstract

In this paper, we prove the existence of solutions for a boundary value problem involving both left Riemann–Liouville and right Caputo fractional derivatives in a weighted space. For this, we convert the posed problem to a sum of of a contraction and a compact operator, then we apply Krasnoselskii’s fixed point theorem to conclude the existence of a nontrivial solution. We end the paper by some numerical examples illustrating the obtained results.

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Acknowledgements

The authors are very grateful to the anonymous referee for his (her) valuable comments and suggestions. This research was done while the first author was visiting the University of Santiago De Compostela, Spain. The hospitality of the host institution and the financial support of Badji Mokhtar Annaba University, Algeria, are gratefully acknowledged.

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Authors and Affiliations

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

    A. Guezane-Lakoud

  2. Departamento de Estadística, Análisis Matemático y Optimización, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782, Santiago de Compostela, Spain

    R. Rodríguez-López

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  1. A. Guezane-Lakoud
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  2. R. Rodríguez-López
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Correspondence to A. Guezane-Lakoud.

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Guezane-Lakoud, A., Rodríguez-López, R. On a fractional boundary value problem in a weighted space. SeMA 75, 435–443 (2018). https://doi.org/10.1007/s40324-017-0142-0

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  • DOI: https://doi.org/10.1007/s40324-017-0142-0

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