The deterministic and stochastic solutions of the Schrodinger equation with time conformable derivative in birefrigent fibers

Zeliha Korpinar; Mustafa Inc; Ali S. Alshomrani; Dumitru Baleanu; Zeliha Korpinar; Mustafa Inc; Ali S. Alshomrani; Dumitru Baleanu

doi:10.3934/math.2020154

AIMS Mathematics

2020, Volume 5, Issue 3: 2326-2345. doi: 10.3934/math.2020154

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The deterministic and stochastic solutions of the Schrodinger equation with time conformable derivative in birefrigent fibers

1.
Mus Alparslan University, Faculty of Economic and Administrative Sciences, Department of Administration, 49250, Muş/Turkiye
2.
Fırat University, Science Faculty, Department of Mathematics, 23119 Elazığ/Turkiye
3.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
4.
King Abdulaziz University, Science Faculty, Department of Mathematics, 21589 Jeddah/ Saudi Arabia
5.
Cankaya University, Science Faculty, Department of Mathematics, 06530 Ankara /Turkiye
6.
Institute of Space Sciences, Magurele-Bucharest, Romania

Received: 14 November 2019 Accepted: 23 February 2020 Published: 03 March 2020
MSC : 35Qxx, 35C08, 35L05

In this manuscript, the deterministic and stochastic nonlinear Schrödinger equation with time conformable derivative is analysed in birefrigent fibers. Hermite transforms, white noise analysis and the modified fractional sub-equation method are used to obtain white noise functional solutions for this equation. These solutions consists of exact stochastic hyperbolic functions, trigonometric functions and wave solutions.
- the stochastic time fractional nonlinear Schr?dinger equation,
- the modified fractional sub-equation method
Citation: Zeliha Korpinar, Mustafa Inc, Ali S. Alshomrani, Dumitru Baleanu. The deterministic and stochastic solutions of the Schrodinger equation with time conformable derivative in birefrigent fibers[J]. AIMS Mathematics, 2020, 5(3): 2326-2345. doi: 10.3934/math.2020154

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Abstract

In this manuscript, the deterministic and stochastic nonlinear Schrödinger equation with time conformable derivative is analysed in birefrigent fibers. Hermite transforms, white noise analysis and the modified fractional sub-equation method are used to obtain white noise functional solutions for this equation. These solutions consists of exact stochastic hyperbolic functions, trigonometric functions and wave solutions.

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