Innovative Computational Approach for fuzzy space-time fractional Telegraph equation via the New Iterative Transform Method

Document Type : Research Paper

Authors

1 Department of Mathematics, New Arts, Commerce, and Science College, Ahmednagar

2 Department of Mathematics, NEW ARTS, COMMERCE, AND SCIENCE COLLEGE, AHMEDNAGAR.

3 Department of mathematics, New Arts, Commerce and Science College, Ahmednagar Maharashtra-414 001

4 Department of mathematics, Mahatma Gandhi Vidyamandirs, Samajshree Prashantdada Hiray Arts, Science and Commerce College, Nampur Tal. Baglan Dist. Nashik 423204

Abstract

In this paper, the Fuzzy Sumudu Transform Iterative method (FSTIM) was applied to find the exact fuzzy solution of the fuzzy space-time fractional telegraph equations using the Fuzzy Caputo Fractional Derivative operator. The Telegraph partial differential equation is a hyperbolic equation representing the reaction-diffusion process in various fields. It has applications in engineering, biology, and Physics. The FSTIM provides a reliable and efficient approach for obtaining approximate solutions to these complex equations improving accuracy and allowing for fine-tuning and optimization for better approximation results.
The work introduces a fuzzy logic-based approach to Sumudu transform iterative methods, offering flexibility and adaptability in handling complex equations. This innovative methodology considers uncertainty and imprecision, providing comprehensive and accurate solutions, and advancing numerical methods. Solving the fuzzy space-time fractional telegraph equation used a fusion of the Fuzzy Sumudu transform and iterative approach. Solution of fuzzy fractional telegraph equation finding analytically and interpreting its results graphically. Throughout the article, whenever we draw graphs, we use Mathematica Software. We successfully employed FSTIM, which is elegant and fast to convergence.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 25 March 2024

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History

  • Receive Date: 24 June 2022
  • Revise Date: 20 January 2024
  • Accept Date: 09 February 2024

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