Analytical solution of time-fractional Schr<i>ö</i>dinger equations via Shehu Adomian Decomposition Method

Mamta Kapoor; Nehad Ali Shah; Wajaree Weera; Mamta Kapoor; Nehad Ali Shah; Wajaree Weera

doi:10.3934/math.20221074

AIMS Mathematics

2022, Volume 7, Issue 10: 19562-19596. doi: 10.3934/math.20221074

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Research article

Analytical solution of time-fractional Schrödinger equations via Shehu Adomian Decomposition Method

1.
Department of Mathematics, Lovely Professional University, Phagwara, Punjab, India
2.
Department of Mechanical Engineering Sejong University, Seoul 05006, South Korea
3.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
^†These authors contributed equally to this work and are co-first authors

Received: 29 June 2022 Revised: 27 July 2022 Accepted: 08 August 2022 Published: 05 September 2022
MSC : 49M27, 35R11

Present research deals with the time-fractional Schrödinger equations aiming for the analytical solution via Shehu Transform based Adomian Decomposition Method [STADM]. Three types of time-fractional Schrödinger equations are tackled in the present research. Shehu transform ADM is incorporated to solve the time-fractional PDE along with the fractional derivative in the Caputo sense. The developed technique is easy to implement for fetching an analytical solution. No discretization or numerical program development is demanded. The present scheme will surely help to find the analytical solution to some complex-natured fractional PDEs as well as integro-differential equations. Convergence of the proposed method is also mentioned.
- time-fractional Schrödinger equations,
- Shehu transform,
- Adomian Decomposition Method,
- graphical presentation,
- tabular analysis,
- convergence property
Citation: Mamta Kapoor, Nehad Ali Shah, Wajaree Weera. Analytical solution of time-fractional Schrödinger equations via Shehu Adomian Decomposition Method[J]. AIMS Mathematics, 2022, 7(10): 19562-19596. doi: 10.3934/math.20221074

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Abstract

Present research deals with the time-fractional Schrödinger equations aiming for the analytical solution via Shehu Transform based Adomian Decomposition Method [STADM]. Three types of time-fractional Schrödinger equations are tackled in the present research. Shehu transform ADM is incorporated to solve the time-fractional PDE along with the fractional derivative in the Caputo sense. The developed technique is easy to implement for fetching an analytical solution. No discretization or numerical program development is demanded. The present scheme will surely help to find the analytical solution to some complex-natured fractional PDEs as well as integro-differential equations. Convergence of the proposed method is also mentioned.

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