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Laplace Fractional Residual Power Series Scheme for Caputo Time-Schrodinger Fractional Equations |
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PP: 177-198 |
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doi:10.18576/pfda/110113
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Author(s) |
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Hussam Aljarrah,
Mohammad Alaroud,
Anuar Ishak,
Maslina Darus,
Shrideh Al-Omari,
Mona Khandaqji,
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Abstract |
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| The time-fractional Schrodinger equations (FSEs) have various applications in quantum mechanics and physical sciences as they describe a wide range of wave propagation phenomena including dust-acoustic, Langmuir and electromagnetic waves in the plasma physics. This article aims to employ the Laplace fractional residual power series (RPS) scheme to derive exact and approximate solutions for the FSEs in a time-Caputo sense following a limit concept. By employing the aforementioned Laplace fractional residual power series method, we establish complex linear and complex nonlinear fractional order models and evaluate efficacy of such a method by conducting numerical experiments as an application. Throughout the furnished computations, we include a comparison between the approximate values and their corresponding exact solutions and obtain some analysis on the absolute error. Moreover, 2D and 3D- graphical representations are introduced to display depiction of the dynamic behaviour of the attained solutions in a specific domain. Further, we confirm reliability of solutions generated by the method of the suggested scheme by comparing them with previously established solutions. Such comparisons are shown to be harmonic with the compared methods, which confirms that the Laplace fractional residual power series approach is an alternative, straightforward, precise and effective for solving both linear and non-linear partial differential equations of fractional order. Moreover, we provide numerical and graphical forms to validate the approach.
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