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Existence and uniqueness of solutions to fractional Langevin equations involving two fractional orders

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Abstract

The solvability of initial value problems for nonlinear Langevin equation involving two fractional orders are discussed in this paper. An existence and uniqueness result for the solution is obtained using the Banach contraction principle. Also, at the end of paper, we present an open problem.

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Acknowledgements

The author would like to thank the anonymous referee(s) for careful corrections, which helped him to improve the manuscript. I would like to express hearty thanks to the associate editor, Prof. Simeon Reich, for his support during the review process.

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  1. Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

    Hamid Baghani

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  1. Hamid Baghani
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Correspondence to Hamid Baghani.

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Baghani, H. Existence and uniqueness of solutions to fractional Langevin equations involving two fractional orders. J. Fixed Point Theory Appl. 20, 63 (2018). https://doi.org/10.1007/s11784-018-0540-7

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  • DOI: https://doi.org/10.1007/s11784-018-0540-7

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