A simple iterative approach for some fractional order models of engineering applications

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. The main topic of this paper is the application of the LA transform (LAT) in combination with the Analytical Adomian polynomials to solve 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 a wide variety of physical and mathematical problems. The solution process is explained in a step-by-step manner, 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 towards the exact solution for fractional-order 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.