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Numerical Solutions of Fractional Differential Equations by Using Fractional Taylor Basis

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IEEE/CAA Journal of Automatica Sinica 2017年第1期4卷 98-106页

作者： Vidhya Saraswathy Krishnasamy Somayeh Mashayekhi Mohsen Razzaghi Department of Mathematics and Statistics Mississippi State University Department of Mathematics Florida State University

In this paper, a new numerical method for solving fractional differential equations(FDEs) is presented. The method is based upon the fractional Taylor basis approximations. The operational matrix of the fractional integration for the fractional Taylor basis is introduced. This matrix is then utilized to reduce the solution of the fractional differential equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of this technique.

关键词： Caputo derivative fractional differential equations(FEDs) fractional Taylor basis operational matrix Riemann-Liouville fractional integral operator

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An online estimator for rotor resistance in vector drives of induction machines based on Walsh functions

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Control Theory and Technology 2014年第4期12卷 402-412页

作者： Hamidreza SHIRAZI Jalal NAZARZADEH Engineering Faculty Shahed University

In a modern electrical driver, rotor field oriented control an appropriate transient response. In this method, the space （RFOC） method has been used to achieve a good performance and vector of the rotor flux comes handy by the rotor resistance value. The rotor resistance is one of the important parameters which varies according to motor speed and room temperature alteration. In this paper, a new on-line estimation method is utilized to obtain the rotor resistance by using Walsh functions domain. The Walsh functions are one of the most applicable functions in piecewise constant basis functions （PCBF） to solve dynamic equations. On the other hand, an integral operational matrix is used to simplify the process and speed of the computation algorithm. The simulations results show that the proposed method is capable of solving the dynamic equations in an electrical machine on a time interval which robustly estimates the rotor resistance in contrast with injection noises.

关键词： Vector control Walsh functions operational matrix Rotor resistance estimation

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A numerical study of the nonlinear fractional mathematical model of tumor cells in presence of chemotherapeutic treatment

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International Journal of Biomathematics 2020年第3期13卷 165-181页

作者： Sachin Kumar Abdon Atangana Government Mahatma Gandhi Memorial Post Graduate College Hoshangabad ItarsiIndia 461111 Faculty of Naturaland Agricultural Sciences Institute for Groundwater Studies University of the Free State Bloemfontein 9300 South Africa

Cancer belongs to the class of discascs which is symbolized by out of control cells *** cells affect DNAs and damage *** exist many treatments avail-able in medical science as radiation therapy,targeted therapy,surgery,palliative care and *** is one of the most popular treatments which depends on the type,location and grade of *** this paper,we are working on modeling and prediction of the effect of chemotherapy on cancer cells using a fractional differen-tial equation by using the differential operator in Caputos *** presented model depicts the interaction between tumor,norrnal and immune cells in a tumor by using a system of four coupled fractional partial differential equations(PDEs).For this system,initial conditions of tumor cells and dimensions are taken in such a way that tumor is spread out enough in size and can be detected easily with the clinical *** operational matrix method with Genocchi polynomials is applied to study this system of fractional PDFs(FPDEs).An operational matrix for *** differentiation is *** the collocation method and using this matrix,the nonlinear system is reduced to a system of algebraic equations,which can be solved using Newton iteration *** salient features of this paper are the pictorial presentations of the numerical solution of the concerned equation for different particular cases to show the effect of fractional exponent on diffusive nature of immune cells,tumor cells,normal cells and chemother-apeutic drug and depict the interaction among immune cells,normal cells and tumor cells in a tumor site.

关键词： Fractional PDE diffusion equation operational matrix Genocchi polynomial collocation method

Block Pulse算子矩阵法求解变系数时间分数阶对流扩散方程（英文）

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高等学校计算数学学报 2019年第4期41卷 346-357页

作者：王进斌马立峰解加全郭蓉太原科技大学机械工程学院太原科技大学重型机械教育部工程研究中心太原理工大学机械与运载工程学院太原科技大学应用科学学院工

The numerical technique based on two-dimensional block pulse functions(2D-BPFs) is proposed for solving the time fractional convection diffusion equations with variable coeficients(FCDEs).We introduce the block pulse operational matrices of the fractional order ***,we translate the original equation into a Sylvester equation by the proposed ***,some numerical examples are given and numerical results are shown to demonstrate the accuracy and reliability of the above-mentioned algorithm.

关键词： Time-fractional convection diffusion equations Block-pulse functions operational matrix Caputo derivative

Numerical Solution for Fractional Partial Differential Equation with Bernstein Polynomials

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Journal of Electronic Science and Technology 2014年第3期12卷 331-338页

作者： Jin-Sheng Wang Li-Qing Liu Yi-Ming Chen Xiao-Hong Ke Institute of School of Continuing Education Yanshan University Institute of College of Science Yanshan University

A framework to obtain numerical solution of the fractional partial differential equation using Bernstein polynomials is presented. The main characteristic behind this approach is that a fractional order operational matrix of Bernstein polynomials is derived. With the operational matrix, the equation is transformed into the products of several dependent matrixes which can also be regarded as the system of linear equations after dispersing the variable. By solving the linear equations, the numerical solutions are acquired. Only a small number of Bernstein polynomials are needed to obtain a satisfactory result. Numerical examples are provided to show that the method is computationally efficient.

关键词： Absolute error Bernstein polynomials fractional partial differential equation numerical solution operational matrix

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