文章基本信息

标题：Elzaki Transform Residual Power Series Method for the Fractional Population Diffusion Equations
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作者：Jianke Zhang ; Xiaoyi Chen ; Lifeng Li 等
期刊名称：Engineering Letters
印刷版ISSN：1816-093X
电子版ISSN：1816-0948
出版年度：2021
卷号：29
期号：4
页码：1561-1572
语种：English
出版社：Newswood Ltd
摘要：Residual power series method(RPSM) is an effective method for solving approximate analytic solutions offractional differential equations(FDEs). However, the (n n 1)αderivative of the residual function is required in this method.As we all know, it is difficult to compute the fractional-orderderivative of a function by computer. This makes the applicationof the classic RPSM limited to a certain extent. To overcomethe difficulty of the RPSM, we combine the Elzaki transformmethod with the RPSM to propose a new method, the Elzakitransform residual power series method(ERPSM). Firstly, theElzaki transform is applied to both sides of the time FDEs.Secondly, the Elzaki inverse is taken on both sides of equationto obtain expression of the solution of the FDEs. Thirdly, thesolution of the FDEs is expanded in fractional power seriesform and substituted into the equation. The unknown coefficientfunction is obtained by setting the residual function as zeroand combining the initial conditions. Finally, the coefficientfunction is substituted into the power series form solution toobtain the finite term approximate analytic solutions. The newmethod is used to solve the time-fractional biological populationdiffusion equation(TFBPDEs). The presented results confirmthe dependability and accuracy of the proposed method. Thismethod does not require calculating the (n n 1)α derivativeof the residual function and is easy to be calculated on thecomputer. The ERPSM has less calculation effort than theclassic RPSM. Some examples are given in datum and images,which are compared with the results of the RPSM and othermethods.
关键词：Residual power series method; Elzaki transform; Time-fractional biological population diffusion equations(TFBPDEs); Caputo derivative