Numerical solution of strongly nonlinear full fractional duffing equation. Issue 8 (16th November 2020)

• Record Type: Journal Article
• Authors: Pirmohabbati, P.; Sheikhani, A. H. Refahi; Najafi, H. Saberi; Ziabari, A. Abdolahzadeh
• Is Part Of: Journal of interdisciplinary mathematics. Volume 23:Issue 8(2020)
• Page Start: 1531
• Page End: 1551
• Publication Date: 2020-11-16
• Subjects: 26A33 -- 97N40 -- 34A08 -- 34A34; Fractional Duffing differential equation -- Block-pulse functions -- Fractional order derivative -- Strongly Nonlinear; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.1080/09720502.2020.1776934
• Languages: English
• ISSNs: 0972-0502

Abstract

Abstract: In this work, based on the operational matrix of fractional order integration, we present an approach for the numerical solution of strongly nonlinear full fractional Duffing equation. For this goal, with respect to the Caputo derivative, we use the block-pulse wavelets matrix of fractional order integration. To obtain this purpose, the errors are analyzed. The method has been considered by some numerical examples and variations in coefficients as well as in the derivative of the equation too. We examine the exact solutions for the equation under study in three different categories including, polynomials, exponential and sinusoidal solutions. It is shown that the suggested method works well.