Numerical Solution of Composite Fractional Oscillation Equation by Fractional Differential Transform Method and Variational Iteration Method

Authors

  • Umme Kulsume Shaun Department of Mathematics, Mawlana Bhashani Science and Technology University, Santosh, Tangail-1902, Bangladesh Author
  • Tahamina Akter Department of Mathematics, Mawlana Bhashani Science and Technology University, Santosh, Tangail-1902, Bangladesh Author
  • Mst. Ruksana Akter Department of Mathematics, Mawlana Bhashani Science and Technology University, Santosh, Tangail-1902, Bangladesh Author
  • Shahana Afroz Department of Mathematics, European University of Bangladesh, Gabtoli, Dhaka-1216, Bangladesh Author
  • Md. Musa Miah Department of Mathematics, Mawlana Bhashani Science and Technology University, Santosh, Tangail-1902, Bangladesh Author

DOI:

https://doi.org/10.69728/jst.v10.53

Keywords:

The Caputo Derivative, Caputo-Fabrizio Derivative, Laplace Operators, Composite Fractional Relaxation Equation, Composite Fractional Oscillation Equation

Abstract

This research aims to find the numerical solution of nonlinear composite fractional oscillation equation using Fractional Differential Transform Method (FDTM) and Variational Iteration Method (VIM). The numerical solutions demonstrate that the two approaches agree fairly well. As a result, these two approaches represent extremely strong and effective methods for resolving various types of fractional differential equations, both linear and non-linear, that arise in numerous technological and engineering domains. We can conclude that both approaches are highly effective and potent in obtaining both numerical and analytical resolutions for a broad range of FDEs. However, the FDTM solves nonlinear problem more closer to the exact solution, giving it an advantage over the VIM.

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Published

31-12-2024

How to Cite

Shaun , U. K., Akter, T., Akter, M. R., Afroz, S., & Miah, M. M. (2024). Numerical Solution of Composite Fractional Oscillation Equation by Fractional Differential Transform Method and Variational Iteration Method. MBSTU Journal of Science and Technology, 10(2), 33-39. https://doi.org/10.69728/jst.v10.53