Abstract
The core aim of this study is to propose a novel computational procedure, namely, Elzaki transform iterative method to work out two‐dimensional nonlinear time‐fractional Zakharov–Kuznetsov equation numerically. We execute the suggested iterative procedure on two models and results are presented graphically in the form of surface plot and absolute error is compared with the VIM and HPM to show that the method is more powerful than VIM and HPM and deduce that the offered numerical pattern is more efficient in simulating linear and nonlinear fractional order models.
Highlights
Applications of fractional calculus are found in various fields such as social science, viscoelasticity, finance, electrochemistry, finance, mathematical physics, signal processing, and physics
We cannot think that any model exits physically without fractional derivatives. ere are numerous nonlinear models in this world, and we say it is not possible to find out the solution analytically of nonlinear fractional models
It has already been proved by many researchers that fractional order generalizations of integral order models portray the natural phenomenon in extremely proficient manner. e classical derivatives exhibit local nature whereas the Caputo fractional derivatives exhibit nonlocal nature
Summary
Applications of fractional calculus are found in various fields such as social science, viscoelasticity, finance, electrochemistry, finance, mathematical physics, signal processing, and physics. We introduced iterative Elzaki transform method to study the numerical solution of two-dimensional nonlinear Zakharov–Kuznetsov equations fractional in time. E vital inspiration to work on this idea is established, a computational procedure to investigate nonlinear fractional differential equations, which is reliable and efficient Since, their application is being found in mathematical modeling of real-world problems. We suggest the iterative Elzaki transform method to numerically solve the nonlinear Zakharov–Kuznetsov equation fractional in time. We are well familiar that integral transform methods are very helpful in finding the solution of linear and nonlinear fractional, ordinary, and partial differential equations. E development of the proposed method is based on combination of two strong methodologies and applicable to work with different types of fractional order linear and nonlinear ordinary and partial differential equation. (8) Local fractional derivative has attracted much attention due to its simple chain rule: g(α) dαg(x) x0
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