scholarly journals REGARDING NEW NUMERICAL RESULTS FOR THE DYNAMICAL MODEL OF ROMANTIC RELATIONSHIPS WITH FRACTIONAL DERIVATIVE

Fractals ◽  
2021 ◽  
pp. 2240009
Author(s):  
WEI GAO ◽  
P. VEERESHA ◽  
D. G. PRAKASHA ◽  
HACI MEHMET BASKONUS
Keyword(s):  
Romantic Relationships ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Real Word ◽  
Transform Method ◽  
Coupled Equations ◽  
Fractional Order Differential Equations ◽  
Analysis Technique ◽  
Homotopy Analysis

The main purpose of the present investigation is to find the solution of fractional coupled equations describing the romantic relationships using [Formula: see text]-homotopy analysis transform method ([Formula: see text]-HATM). The considered scheme is a unification of [Formula: see text]-homotopy analysis technique with Laplace transform (LT). More preciously, we scrutinized the behavior of the obtained solution for the considered model with fractional-order, in order to elucidate the effectiveness of the proposed algorithm. Further, for the different fractional-order and parameters offered by the considered method, the physical natures have been apprehended. The obtained consequences evidence that the proposed method is very effective and highly methodical to study and examine the nature and its corresponding consequences of the system of fractional order differential equations describing the real word problems.

The Error Incurred in Using the Caputo-Derivative Laplace-Transform

2009 ◽  
Author(s):  
Tom T. Hartley ◽  
Carl F. Lorenzo
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Caputo Derivative ◽  
Fractional Order Differential Equations ◽  
Definition Of

This paper considers the initialization of fractional-order differential equations. The initialization responses obtained using the Caputo derivative are compared with the exact initialization responses from the Riemann-Liouville definition of the fractional derivative. The error incurred in using the Caputo derivative for initialization problems in fractionalorder differential equations is presented.

Homotopy analysis transform algorithm to solve time-fractional foam drainage equation

2016 ◽  
Vol 5 (3) ◽  
Author(s):  
Mukesh Singh ◽  
Mohd Naseem ◽  
Amit Kumar ◽  
Sunil Kumar
Keyword(s):  
Laplace Transform ◽  
Fractional Derivative ◽  
Homotopy Analysis Method ◽  
Present Method ◽  
Analysis Method ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Homotopy Analysis ◽  
Foam Drainage Equation ◽  
Foam Drainage

AbstractThis paper emphasizes on finding the solution for a foam drainageequation using the technique of modified homotopy analysis transform method (MHATM). MHATM is a new amalgamation of the homotopy analysis method and Laplace transform method with homotopy polynomial. Comparisons are made between the results of the proposed method for different values of fractional derivative α and exact solutions. Then, we analyze the results by numerical simulations, which demonstrate the simplicity and effectiveness of the present method.

Numerical approximation of Newell-Whitehead-Segel equation of fractional order

2016 ◽  
Vol 5 (2) ◽  
Author(s):  
Devendra Kumar ◽  
Ram Prakash Sharma
Keyword(s):  
Fractional Order ◽  
Homotopy Analysis Method ◽  
Numerical Solutions ◽  
Analysis Method ◽  
Transform Method ◽  
Analysis Technique ◽  
Homotopy Analysis ◽  
Sumudu Transform ◽  
Linear Differential ◽  
User Friendly

AbstractThe aim of the present work is to propose a user friendly approach based on homotopy analysis method combined with Sumudu transform method to drive analytical and numerical solutions of the fractional Newell-Whitehead-Segel amplitude equation which describes the appearance of the stripe patterns in 2-dimensional systems. The coupling of homotopy analysis method with Sumudu transform algorithm makes the calculation very easy. The proposed technique gives an analytic solution in the form of series which converge very fastly. The analytical and numerical results reveal that the coupling of homotopy analysis technique with Sumudu transform algorithm is very easy to apply and highly accuratewhen apply to non-linear differential equation of fractional order.

scholarly journals Extension of natural transform method with Daftardar-Jafari polynomials for fractional order differential equations

2021 ◽  
Vol 60 (3) ◽  
pp. 3205-3217
Author(s):  
Rashid Nawaz ◽  
Nasir Ali ◽  
Laiq Zada ◽  
Kottakkkaran Sooppy Nisar ◽  
M.R. Alharthi ◽  
...  
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Transform Method ◽  
Fractional Order Differential Equations

scholarly journals Darcy–Forchheimer Radiative Flow of Micropoler CNT Nanofluid in Rotating Frame with Convective Heat Generation/Consumption

Processes ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 666 ◽  
Author(s):  
Ebraheem O. Alzahrani ◽  
Zahir Shah ◽  
Wajdi Alghamdi ◽  
Malik Zaka Ullah
Keyword(s):  
Heat Generation ◽  
High Surface ◽  
High Surface Area ◽  
Numerical Results ◽  
Coupled Equations ◽  
Analysis Technique ◽  
Homotopy Analysis ◽  
Material Energy ◽  
The Impact ◽  
Thermal Radiation Effect

Since 1991, from the beginning of the carbon nanotube era, this has been a focus point for investigation due to its synthetic and simple nature. Unique properties like good stiffness, high surface area, and resilience of carbon nanotubes (CNTs) have been investigated in many engineering applications such as hydrogen storage, composite material, energy storage, electrochemical super-capacitors, transistors, sensors, and field-emitting devices. Keeping in view these applications, we investigate single and multi-walled CNTs nanofluid flow having water as the base fluid between parallel and horizontal rotating plates with microstructure and inertial properties. The thermal radiation effect is considered for variable phenomenon of heat generation/consumption. The principal equations are first symmetrically transformed to a system of nonlinear coupled ordinary differential equations (ODEs), and then, Homotopy Analysis Technique (HAM) and numerical method are employed for solving these coupled equations. The obtained analytical and numerical results are explained graphically and through different tables. The HAM and numerical results show an excellent agreement. The Skin friction and the Nusselt number are numerically calculated and then analyzed with the already published results, and these results are found to be in agreement with one another. The impact of important parameters are shown graphically.

An Efficient Technique for Fractional Coupled System Arisen in Magnetothermoelasticity With Rotation Using Mittag–Leffler Kernel

2020 ◽  
Vol 16 (1) ◽  
Author(s):  
P. Veeresha ◽  
D. G. Prakasha ◽  
Dumitru Baleanu
Keyword(s):  
Fractional Order ◽  
Nonlinear Differential Equations ◽  
Coupled System ◽  
Order Model ◽  
Science And Engineering ◽  
Transform Method ◽  
Fractional Order Model ◽  
Analysis Scheme ◽  
Laplace Transform Technique ◽  
Homotopy Analysis

Abstract In this paper, we find the solution for fractional coupled system arisen in magnetothermoelasticity with rotation using q-homotopy analysis transform method (q-HATM). The proposed technique is graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme, and fractional derivative defined with Mittag–Leffler kernel. The fixed point hypothesis is considered to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. To illustrate the efficiency of the future technique, we analyzed the projected model in terms of fractional order. Moreover, the physical behavior of q-HATM solutions has been captured in terms of plots for different arbitrary order. The attained consequences confirm that the considered algorithm is highly methodical, accurate, very effective, and easy to implement while examining the nature of fractional nonlinear differential equations arisen in the connected areas of science and engineering.

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.

scholarly journals Solving smoking epidemic model of fractional order using a modified homotopy analysis transform method

2019 ◽  
Vol 13 (2) ◽  
pp. 115-128 ◽  
Author(s):  
P. Veeresha ◽  
D. G. Prakasha ◽  
Haci Mehmet Baskonus
Keyword(s):  
Fractional Order ◽  
Epidemic Model ◽  
Transform Method ◽  
Homotopy Analysis

scholarly journals Approximate Solutions to Time-Fractional Schrödinger Equation via Homotopy Analysis Method

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Najeeb Alam Khan ◽  
Muhammad Jamil ◽  
Asmat Ara
Keyword(s):  
Homotopy Analysis Method ◽  
Fractional Derivatives ◽  
Approximate Solutions ◽  
Higher Dimensions ◽  
Analysis Method ◽  
Transform Method ◽  
Coupled Equations ◽  
Fractional Schrödinger Equations ◽  
Differential Transform ◽  
Homotopy Analysis

We construct the approximate solutions of the time-fractional Schrödinger equations, with zero and nonzero trapping potential, by homotopy analysis method (HAM). The fractional derivatives, in the Caputo sense, are used. The method is capable of reducing the size of calculations and handles nonlinear-coupled equations in a direct manner. The results show that HAM is more promising, convenient, efficient and less computational than differential transform method (DTM), and easy to apply in spaces of higher dimensions as well.

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