Abstract
In this paper, we introduce the Yang transform homotopy perturbation method (YTHPM), which is a novel method. We provide formulae for the Yang transform of Caputo-Fabrizio fractional order derivatives. We derive an algorithm for the solution of Caputo-Fabrizio (CF) fractional order partial differential equation in series form and show its convergence to the exact solution. To demonstrate the novel approach, we include some examples with detailed solutions. We use tables and graphs to compare the exact and approximate solutions.
Highlights
Introduction and MotivationNoninteger calculus is a popular field that is aimed at explaining real-world phenomena that are modeled with operators of fractional order
A general procedure for solving nonlinear PDEs described by the CF derivative has been developed
We have demonstrated the estimated solution’s convergence and provided a result for the absolute error calculation
Summary
Noninteger calculus is a popular field that is aimed at explaining real-world phenomena that are modeled with operators of fractional order. Caputo and Fabrizio (CF) [12] suggested a new fractional operator with an exponential kernel in a recent attempt around the middle of the last decade This derivative’s kernel is nonsingular, so the results are more reasonable than the classical one. Differential equations of fractional order are notoriously difficult to solve, and finding an exact solution is even more difficult. Elzaki introduced new integral transform “Elzaki Transform” and used heavily in solving partial differential equations [18]. The main purpose of this article is to apply newly introduced integral transform called “Yang Transform” discovered by Yang [24] with HPM to solve nonlinear fractional order PDEs. We solve two popular nonlinear PDEs through the proposed method. There is no requirement for a method like discretizing the problem and no linearization for the nonlinear problem, and just a few iterations can lead to a solution that can be estimated using these techniques
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
