Adapting Laplace residual power series approach to the Caudrey Dodd Gibbon equation

• Published in: Scientific reports Vol. 14; no. 1; p. 9772
• Main Authors: Abdelhafeez, Samy A., Arafa, Anas A. M., Zahran, Yousef H., Osman, Ibrahim S. I., Ramadan, Moutaz
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 29.04.2024; Nature Publishing Group; Nature Portfolio
• Subjects: 639/166; 639/705; Calculus; Caudrey Dodd Gibbon equation; Differential equations; Fractional derivatives; Graphs; Humanities and Social Sciences; Laplace transform; Laplace transforms; Mathematics; multidisciplinary; Numerical results; Partial differential equations; Residual power series method; Science; Science (multidisciplinary); Residual power series method; Laplace transform; Caudrey Dodd Gibbon equation; Fractional derivatives; Numerical results
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/s41598-024-57780-x

In real-life applications, nonlinear differential equations play an essential role in representing many phenomena. One well-known nonlinear differential equation that helps describe and explain many chemicals, physical, and biological processes is the Caudrey Dodd Gibbon equation (CDGE). In this paper, we propose the Laplace residual power series method to solve fractional CDGE. The use of terms that involve fractional derivatives leads to a higher degree of freedom, making them more realistic than those equations that involve the derivation of an integer order. The proposed method gives an easy and faster solution in the form of fast convergence. Using the limit theorem of evaluation, the experimental part presents the results and graphs obtained at several values of the fractional derivative order.