scholarly journals Homotopy Series Solutions to Time-Space Fractional Coupled Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
Jin Zhang ◽  
Ming Cai ◽  
Bochao Chen ◽  
Hui Wei
Keyword(s):  
Water System ◽  
Coupled System ◽  
Coupled Systems ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Time Space ◽  
Nonlinear Coupled System ◽  
Sumudu Transform ◽  
Shallow Water System ◽  
Burgers System

We apply the homotopy perturbation Sumudu transform method (HPSTM) to the time-space fractional coupled systems in the sense of Riemann-Liouville fractional integral and Caputo derivative. The HPSTM is a combination of Sumudu transform and homotopy perturbation method, which can be easily handled with nonlinear coupled system. We apply the method to the coupled Burgers system, the coupled KdV system, the generalized Hirota-Satsuma coupled KdV system, the coupled WBK system, and the coupled shallow water system. The simplicity and validity of the method can be shown by the applications and the numerical results.

scholarly journals Approximate solution for fractional attractor one-dimensional Keller-Segel equations using homotopy perturbation sumudu transform method

2020 ◽  
Vol 9 (1) ◽  
pp. 370-381
Author(s):  
Dinkar Sharma ◽  
Gurpinder Singh Samra ◽  
Prince Singh
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Simple Technique ◽  
Nonlinear Partial Differential Equations ◽  
Transform Method ◽  
Present Scheme ◽  
One Dimensional ◽  
Homotopy Perturbation ◽  
Sumudu Transform

AbstractIn this paper, homotopy perturbation sumudu transform method (HPSTM) is proposed to solve fractional attractor one-dimensional Keller-Segel equations. The HPSTM is a combined form of homotopy perturbation method (HPM) and sumudu transform using He’s polynomials. The result shows that the HPSTM is very efficient and simple technique for solving nonlinear partial differential equations. Test examples are considered to illustrate the present scheme.

scholarly journals On the Solution of an Imprecisely Defined Nonlinear Time-Fractional Dynamical Model of Marriage

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 689 ◽  
Author(s):  
Rajarama Mohan Jena ◽  
Snehashish Chakraverty ◽  
Dumitru Baleanu
Keyword(s):  
Dynamical System ◽  
Fuzzy Numbers ◽  
Initial Conditions ◽  
Coupled System ◽  
Dynamical Model ◽  
Transform Method ◽  
System Parameters ◽  
Nonlinear Coupled System ◽  
Differential Transform ◽  
Fractional Dynamical System

The present paper investigates the numerical solution of an imprecisely defined nonlinear coupled time-fractional dynamical model of marriage (FDMM). Uncertainties are assumed to exist in the dynamical system parameters, as well as in the initial conditions that are formulated by triangular normalized fuzzy sets. The corresponding fractional dynamical system has first been converted to an interval-based fuzzy nonlinear coupled system with the help of a single-parametric gamma-cut form. Further, the double-parametric form (DPF) of fuzzy numbers has been used to handle the uncertainty. The fractional reduced differential transform method (FRDTM) has been applied to this transformed DPF system for obtaining the approximate solution of the FDMM. Validation of this method was ensured by comparing it with other methods taking the gamma-cut as being equal to one.

scholarly journals Analytical Solution of Space-Time Fractional Fokker-Planck Equation by Homotopy Perturbation Sumudu Transform Method

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Ravi Shanker Dubey ◽  
Badr Saad T. Alkahtani ◽  
Abdon Atangana
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Planck Equation ◽  
Space Time ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
He’S Polynomials ◽  
Sumudu Transform ◽  
Fokker Planck Equations ◽  
Fokker Planck

An efficient approach based on homotopy perturbation method by using Sumudu transform is proposed to solve some linear and nonlinear space-time fractional Fokker-Planck equations (FPEs) in closed form. The space and time fractional derivatives are considered in Caputo sense. The homotopy perturbation Sumudu transform method (HPSTM) is a combined form of Sumudu transform, homotopy perturbation method, and He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. Some examples show that the HPSTM is an effective tool for solving many space time fractional partial differential equations.

scholarly journals Semi- analytic numerical method for solution of time-space fractional heat and wave type equations with variable coefficients

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 74-86 ◽  
Author(s):  
Rishi Kumar Pandey ◽  
Hradyesh Kumar Mishra
Keyword(s):  
Fractional Derivative ◽  
Series Solution ◽  
Variable Coefficients ◽  
Variable Order ◽  
Wave Type ◽  
Transform Method ◽  
Time Space ◽  
Homotopy Analysis ◽  
Sumudu Transform ◽  
Variable Order Derivative

AbstractThe time and space fractional wave and heat type equations with variable coefficients are considered, and the variable order derivative in He‘s fractional derivative sense are taken. The utility of the homotopy analysis fractional sumudu transform method is shown in the form of a series solution for these generalized fractional order equations. Some discussion with examples are presented to explain the accuracy and ease of the method.

Hermite collocation method for obtaining the chaotic behavior of a nonlinear coupled system of FDEs

2020 ◽  
Vol 31 (07) ◽  
pp. 2050093
Author(s):  
M. M. Khader ◽  
Mohammed M. Babatin
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Chaotic Behavior ◽  
Standard Form ◽  
Coupled System ◽  
Coupled Systems ◽  
Electrical Network ◽  
Algebraic Equations ◽  
Home Heating ◽  
Nonlinear Coupled System

This paper is devoted to introduce an efficient solver using the Hermite collocation technique (HCT), of the coupled system of fractional differential equations (FDEs). The given systems are of basic importance in modeling various phenomena like Cascades and Compartment Analysis, Pond Pollution, Home Heating, Chemostats, and Microorganism Culturing, Nutrient Flow in an Aquarium, Biomass Transfer, Forecasting Prices, Electrical Network, Earthquake Effects on Buildings. The proposed method reduces the system of FDEs to a system of algebraic equations in the coefficients of the expansion using the Hermite polynomials. The introduced method is computer oriented and provides highly accurate solution. To demonstrate the efficiency of the method, two examples are solved and the results are displayed graphically. Finally, we convert the presented coupled systems from the case of its standard form to a first-order ordinary differential equations to compare the obtained numerical solutions with those solutions using the fourth-order Runge–Kutta method (RK4).

APPLICATION OF AN EFFECTIVE METHOD ON THE SYSTEM OF NONLINEAR FUZZY INTEGRO-DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 21 (2) ◽  
pp. 407-422
Author(s):  
ANGBEEN IQBAL ◽  
JAMSHAD AHMAD ◽  
QAZI MAHMOOD UL HASSAN
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Graphical Representation ◽  
Numerical Approach ◽  
Fuzzy Arithmetic ◽  
Transform Method ◽  
Numerical Examples ◽  
Homotopy Perturbation ◽  
Sumudu Transform ◽  
Fuzzy Parameter

In real world physical applications purpose, it is complicated to acquire an exact solution of fuzzy differential equations due to complexities in fuzzy arithmetic and therefore creating the need for the use of reliable and efficient techniques in the solution of fuzzy differential equations. The purpose of this research paper is to utilize the reliable analytic approach of homotopy perturbation Sumudu transform method for better understanding of systems of non-linear fuzzy integro-differential equations, while using the concept of fuzzy parameter in certain dynamical problems to remove the hurdles faced in numerical approach. These mathematical models are of great interest in engineering and physics. Some numerical examples are also given to demonstrate the efficiency and superiority of the method, followed by graphical representation of the comparison of exact and approximated solution by using Maple 2017

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