10.57647/cna.2025.bcr2-d739

Benefaction of Rothe's Time Discretization Method to Solve Diffusion Equation Involving Riemann-Liouville Fractional Integral and Delay Integral Function

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  • Nishi Gupta*1,
  1. Department of Mathematics,Indian Institute of Technology Guwahati,Assam India

Received: 2024-12-30

Accepted: 2025-01-22

Published in Issue 2025-06-30

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Benefaction of Rothe’s Time Discretization Method to Solve Diffusion Equation Involving Riemann-Liouville Fractional Integral and Delay Integral Function. (2025). Communications in Nonlinear Analysis, 13(1), 26-36. https://doi.org/10.57647/cna.2025.bcr2-d739

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Abstract

This paper presents a diffusion equation involving $\alpha^{th}$ order Riemann-Liouville (R-L) fractional integral along with integral forcing function for delay and some constant coefficients. We apply $L2$ scheme to discretize the fractional integral function and Rothe's method  is opted to establish the existence and uniqueness of a strong solution. In addition, we provide some error estimation and continuous on initial data. Eventually, we provide an application to manifest the results.

Keywords

  • Method of semidiscretization,
  • Riemann-Liouville fractional integral,
  • Strong solution,
  • Delay differential equation,
  • Initial conditions
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