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A different approach for conformable fractional biochemical reaction–diffusion models

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Applied Mathematics(A Journal of Chinese Universities) 2020年第4期35卷 452-467页

作者： Anas Arafa Department of Mathematics and Computer Science Faculty of SciencePort Said UniversityPort SaidEgypt

This paper attempts to shed light on three biochemical reaction-diffusion models:conformable fractional Brusselator,conformable fractional Schnakenberg,and conformable fractional *** is done using conformable residual power series(hence-form,CRPS)technique which has indeed,proved to be a useful tool for generating the ***,CRPS is an effective method of solving nonlinear fractional differential equations with greater accuracy and ease.

关键词： Brusselator model Schnakenberg model Gray-Scott model conformable fractional derivatives residual power series method

An attractive analytical technique for coupled system of fractional partial differential equations in shallow water waves with conformable derivative

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Communications in Theoretical Physics 2020年第8期72卷 1-17页

作者： Mohammed Al-Smadi Omar Abu Arqub Samir Hadid Department of Applied Science Ajloun CollegeAl-Balqa Applied UniversityAjloun 26816Jordan Department of Mathematics Faculty of ScienceAl-Balqa Applied UniversitySalt 19117Jordan Department of Mathematics and Sciences College of Humanities and SciencesAjman UniversityAjmanUnited Arab Emirates

Mathematical simulation of nonlinear physical and abstract systems is a very vital process for predicting the solution behavior of fractional partial differential equations(FPDEs)corresponding to different applications in science and engineering. In this paper, an attractive reliable analytical technique, the conformable residual power series, is implemented for constructing approximate series solutions for a class of nonlinear coupled FPDEs arising in fluid mechanics and fluid flow, which are often designed to demonstrate the behavior of weakly nonlinear and long waves and describe the interaction of shallow water waves. In the proposed technique the n-truncated representation is substituted into the original system and it is assumed the(n-1) conformable derivative of the residuum is zero. This allows us to estimate coefficients of truncation and successively add the subordinate terms in the multiple fractional power series with a rapidly convergent form. The influence, capacity, and feasibility of the presented approach are verified by testing some real-world applications. Finally, highlights and some closing comments are attached.

关键词： nonlinear coupled system fractional partial differential equations residual power series method conformable fractional derivative

New Analytical and Numerical Results For Fractional Bogoyavlensky-Konopelchenko Equation Arising in Fluid Dynamics

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Applied Mathematics(A Journal of Chinese Universities) 2020年第1期35卷 101-112页

作者： Ali Kurt Department of Mathematics Pamukkale UniversityDenizli 20180Turkey

In this article,(2+1)-dimensional time fractional Bogoyavlensky-Konopelchenko(BK)equation is studied,which describes the interaction of wave propagating along the x axis and y *** acquire the exact solutions of BK equation we employed sub equation method that is predicated on Riccati equation,and for numerical solutions the residual power series method is *** graphical results that compares the numerical and analytical solutions are given for di erent values of.Also comparative table for the obtained solutions is presented.

关键词： Conformable Fractional Derivative Fractional Bogoyavlensky-Konopelchenko Equation Sub-Equation method residual power series method

Analytical and approximate solutions of(2+1)-dimensional time-fractional Burgers-Kadomtsev-Petviashvili equation

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Communications in Theoretical Physics 2020年第5期72卷 21-31页

作者： Mehmet Senol Department of Mathematics Nevsehir Haci Bektas Veli UniversityNevsehirTurkey

In this paper,we applied the sub-equation method to obtain a new exact solution set for the extended version of the time-fractional Kadomtsev-Petviashvili equation,namely Burgers-Kadomtsev-Petviashvili equation(Burgers-K-P)that arises in shallow water ***,using the residual power series method(RPSM),approximate solutions of the equation were obtained with the help of the Mathematica symbolic computation *** also presented a few graphical illustrations for some *** fractional derivatives were considered in the conformable *** of the obtained solutions were replaced back in the governing equation to check and ensure the reliability of the *** numerical outcomes confirmed that both methods are simple,robust and effective to achieve exact and approximate solutions of nonlinear fractional differential equations.

关键词： fractional partial differential equations Burgers-Kadomtsev-Petviashvili equation conformable fractional derivative sub-equation method residual power series method