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Existence Results for Langevin Equation Involving Atangana-Baleanu Fractional Operators

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Department of Mathematics, Cankaya University, 06790 Ankara, Turkey
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Institute of Space Sciences, 077125 Magurele-Bucharest, Romania
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Department of Medical Research, China Medical University, Taichung 40447, Taiwan
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Department of Mathematics, Neka Branch, Islamic Azad University, Neka, Iran
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Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(3), 408; https://doi.org/10.3390/math8030408 (registering DOI)
Received: 28 January 2020 / Revised: 21 February 2020 / Accepted: 25 February 2020 / Published: 12 March 2020
(This article belongs to the Section Difference and Differential Equations)
A new form of nonlinear Langevin equation (NLE), featuring two derivatives of non-integer orders, is studied in this research. An existence conclusion due to the nonlinear alternative of Leray-Schauder type (LSN) for the solution is offered first and, following that, the uniqueness of solution using Banach contraction principle (BCP) is demonstrated. Eventually, the derivatives of non-integer orders are elaborated in Atangana-Baleanu sense. View Full-Text
Keywords: Atangana-Baleanu fractional derivative; Langevin equation; Leray-Schauder nonlinear; existence results Atangana-Baleanu fractional derivative; Langevin equation; Leray-Schauder nonlinear; existence results
MDPI and ACS Style

Baleanu, D.; Darzi, R.; Agheli, B. Existence Results for Langevin Equation Involving Atangana-Baleanu Fractional Operators. Mathematics 2020, 8, 408.

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