Abstract
The objective of this paper is to compute the new modified method of variational iteration and the Laplace Adomian decomposition method for the solution of nonlinear fractional partial differential equations. We execute a comparatively newfangled analytical mechanism that is denoted by the modified Laplace variational iteration method (MLVIM) and Laplace Adomian decomposition method (LADM). The effect of the numerical results indicates that the double approximation is handy to execute and reliable when applied. It is shown that numerical solutions are gained in the form of approximately series which are facilely computable.
Highlights
Fractional calculus has tremendous applications in applied science such as mechanical engineering, heat conduction, viscoelasticity, electrode-electrolyte polarization, nanotechnology, diffusion equations, and nearly every part of science and technology
One of the most important uses of fractional calculus is in fractional partial differential equations (PDEs) as most natural phenomena could be modeled by PDEs
Contemporary improvements of fractional differential equations are supported by the earliest examples of applications in scientific fields, such Liouville’s example
Summary
Fractional calculus has tremendous applications in applied science such as mechanical engineering, heat conduction, viscoelasticity, electrode-electrolyte polarization, nanotechnology, diffusion equations, and nearly every part of science and technology. The nonlinear oscillation could be represented by fractional derivatives and the fluid dynamic traffic pattern with fractional derivatives [5, 6]; this leads to the use of FPDEs. Several of the main tools used in solving this type of equations are LADM, VIM, and homotopy. LADM and the VIM are comparatively new approaches to fit an analytical approximation to linear and nonlinear problems [8,9,10,11,12]. They have been concerned with the solution of Caputo fractional integrodifferential equations by the modified variational iteration technique via the Laplace approach [17].
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.
