Nehad safwat abdelmohsen
Demonstrator
A simple iterative approach for some fractional order models of engineering applications
• 2024
Publication Information
Authors
Nehad S. El Said, Mourad S. Semary, D. A. Hammad , M. S. El-Azab
Keywords
LA transformation, fractional-order partial differential equations, Integral transform methods, Navier-Stokes
equation
Journal
Not Available
Publisher
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Volume
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Issue
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Pages
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publication.type
Local
Paper Link
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Supplementary Materials
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Abstract
The main topic of this paper is implementing an iterative approach based on the LA transformation (LAT) for solving
fractional order-partial differential equations (FO-PDEs) offering valuable insights and practical solutions for a wide range of
scientific and engineering applications. Several examples are presented, covering various physical and mathematical problems.
The solution process is explained step-by-step, depicting how LAT can effectively handle fractional-order derivatives and achieve
efficient approximated and analytical solutions. The Caputo operator is utilized to express the fractional-order derivatives. The
paper explores various examples involving fractional diffusion equations, fractional Burger’s equation, and fractional Navier-
Stokes equation, among others. This method ensures convergence toward the exact solution for FO-PDEs and has been validated
through the presentation of several examples that demonstrate its accuracy. This study contributes to the advancement of
fractional calculus techniques and their utilization in real-world problem-solving scenarios
fractional order-partial differential equations (FO-PDEs) offering valuable insights and practical solutions for a wide range of
scientific and engineering applications. Several examples are presented, covering various physical and mathematical problems.
The solution process is explained step-by-step, depicting how LAT can effectively handle fractional-order derivatives and achieve
efficient approximated and analytical solutions. The Caputo operator is utilized to express the fractional-order derivatives. The
paper explores various examples involving fractional diffusion equations, fractional Burger’s equation, and fractional Navier-
Stokes equation, among others. This method ensures convergence toward the exact solution for FO-PDEs and has been validated
through the presentation of several examples that demonstrate its accuracy. This study contributes to the advancement of
fractional calculus techniques and their utilization in real-world problem-solving scenarios