α-Transform Method for Solving Fractional Wave Equation Using α-Fractional Derivative
DOI:
https://doi.org/10.112222/ijits.v1.i1.18794Keywords:
α-Fractional Derivative, ODEs, PDEs, FPDEs, MOLAbstract
Differential equation (DE) plays a big role in applied science and engineering. One important topic and an extensive field of research involves determining the analytical or numerical solutions to the DEs. Utilizing the α-fractional derivative definition to transform the quasi-linear fractional partial differential equation (FPDE) to a quasi-linear partial differential equation (PDE) and then, solving a quasi-linear PDE utilizing the method of lines (MOL) is the objective of this article. The definition of the α-fractional derivative has appropriate, essential, and strong qualities. Furthermore, a quasi-linear PDE is generated from a quasi-linear FPDE using the characteristics of the definition of the α-fractional derivative. A system of ordinary differential equations (ODEs) can therefore be constructed from the PDE by employing the MOL. After applying the proposed approach to solve an implementation, the exact solution is compared to the numerical solution. Based on the test implementation, the recommended approach performs well with its solution. Consequently, the algorithm employed for this method has been shown to be accurate and efficient.
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