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<p>This paper presents numerical solutions for linear and nonlinear fractional partial differential equations (Cauchy reaction diffusion) applying an approximation method called the Least Square Residual Power Series Method (LSRPSM). In addition to presenting the fractional Wronskian definition, the Caputo sense has been used to evaluate the fractional order derivative operator. The Least Squares Method (LSM) and the Residual Power Series Method (RPSM) are combined in this flexible technique. Consequently, we produced a rapidly convergent series with clearly defined elements for the time fractional Cauchy Reaction Diffusion Equations (CRDEs). Compared to exact solutions, RPSM and Elzaki residual power series method (ERPSM). The LSRPSM provides sufficient accuracy when applied to approximation solutions. The numerical solutions to fractional partial differential equations and their graphical representations will be covered in our final section. We are charting the outcomes of each of the partial fraction differential equations to show that MATLAB produces superior results.</p>

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Comparative numerical study of caputo time-fractional reaction–diffusion equations with applications in physical phenomena

  • 期刊论文

  • 发表日期：

    2026年6月23日

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  • Ahmed Hassan

摘要

This paper presents numerical solutions for linear and nonlinear fractional partial differential equations (Cauchy reaction diffusion) applying an approximation method called the Least Square Residual Power Series Method (LSRPSM). In addition to presenting the fractional Wronskian definition, the Caputo sense has been used to evaluate the fractional order derivative operator. The Least Squares Method (LSM) and the Residual Power Series Method (RPSM) are combined in this flexible technique. Consequently, we produced a rapidly convergent series with clearly defined elements for the time fractional Cauchy Reaction Diffusion Equations (CRDEs). Compared to exact solutions, RPSM and Elzaki residual power series method (ERPSM). The LSRPSM provides sufficient accuracy when applied to approximation solutions. The numerical solutions to fractional partial differential equations and their graphical representations will be covered in our final section. We are charting the outcomes of each of the partial fraction differential equations to show that MATLAB produces superior results.