A new iterative method with ρ-Laplace transform for solving fractional differential equations with Caputo generalized fractional derivative

• Published in: Engineering with computers 2022-06, Vol.38 (3), p.2125-2138
• Main Authors: Bhangale, Nikita, Kachhia, Krunal B., Gómez-Aguilar, J. F.
• Format: Article
• Language: English
• Subjects: CAE) and Design; Calculus; Calculus of Variations and Optimal Control; Optimization; Classical Mechanics; Computer Science; Computer-Aided Engineering (CAD; Control; Differential equations; Engineering; Exact solutions; Fractional calculus; Graphical representations; Iterative methods; Laplace transforms; Math. Applications in Chemistry; Mathematical analysis; Mathematical and Computational Engineering; Original Article; Partial differential equations; Physics; Systems Theory
• ISSN: 0177-0667; 1435-5663
• DOI: 10.1007/s00366-020-01202-9

In this paper, the new iterative method with ρ -Laplace transform of getting the approximate solution of fractional differential equations was proposed with Caputo generalized fractional derivative. The effect of the various value of order α and parameter ρ in the solution of certain well known fractional differential equation with Caputo generalized fractional derivative. Applications to the certain fractional differential equation in various systems demonstrate that the proposed method is more reliable and powerful. The graphical representations of the approximate analytic solutions of the fractional differential equations described by the Caputo generalized fractional derivative were provided and the nature of the achieved solution in terms of plots for distinct arbitrary order is captured.