scholarly journals Solving PDEs of fractional order using the unified transform method

2018 ◽  
Vol 339 ◽  
pp. 738-749 ◽  
Author(s):  
Arran Fernandez ◽  
Dumitru Baleanu ◽  
Athanassios S. Fokas
Keyword(s):  
Fractional Order ◽  
Transform Method ◽  
Unified Transform Method

scholarly journals An efficient approach for solution of fractional-order Helmholtz equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nehad Ali Shah ◽  
Essam R. El-Zahar ◽  
Mona D. Aljoufi ◽  
Jae Dong Chung
Keyword(s):  
Perturbation Method ◽  
Fractional Order ◽  
Homotopy Perturbation Method ◽  
Hybrid Technique ◽  
Science And Engineering ◽  
Helmholtz Equations ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Suggested Technique ◽  
Present Technique

AbstractIn this article, a hybrid technique called the homotopy perturbation Elzaki transform method has been implemented to solve fractional-order Helmholtz equations. In the hybrid technique, the Elzaki transform method and the homotopy perturbation method are amalgamated. Three problems are solved to validate and demonstrate the efficacy of the present technique. It is also demonstrated that the results obtained from the suggested technique are in excellent agreement with the results by other techniques. It is shown that the proposed method is efficient, reliable and easy to implement for various related problems of science and engineering.

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 Aboodh Transform Iterative Method for Spatial Diffusion of a Biological Population with Fractional-Order

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 155
Author(s):  
Gbenga O. Ojo ◽  
Nazim I. Mahmudov
Keyword(s):  
Iterative Method ◽  
Fractional Order ◽  
Population Model ◽  
Numerical Solutions ◽  
Computational Effort ◽  
Spatial Diffusion ◽  
Transform Method ◽  
Biological Population ◽  
The Laplace Transform ◽  
New Iterative Method

In this paper, a new approximate analytical method is proposed for solving the fractional biological population model, the fractional derivative is described in the Caputo sense. This method is based upon the Aboodh transform method and the new iterative method, the Aboodh transform is a modification of the Laplace transform. Illustrative cases are considered and the comparison between exact solutions and numerical solutions are considered for different values of alpha. Furthermore, the surface plots are provided in order to understand the effect of the fractional order. The advantage of this method is that it is efficient, precise, and easy to implement with less computational effort.

scholarly journals NUMERICAL SOLUTION FOR TIME-FRACTIONAL MURRAY REACTION-DIFFUSION EQUATIONS VIA REDUCED DIFFERENTIAL TRANSFORM METHOD

2021 ◽  
Author(s):  
Muhammed Yiğider ◽  
Serkan Okur
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Differential Transform Method ◽  
Reaction Diffusion Equations ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential ◽  
Reduced Differential Transform Method ◽  
Time Fractional Differential Equations

In this study, solutions of time-fractional differential equations that emerge from science and engineering have been investigated by employing reduced differential transform method. Initially, the definition of the derivatives with fractional order and their important features are given. Afterwards, by employing the Caputo derivative, reduced differential transform method has been introduced. Finally, the numerical solutions of the fractional order Murray equation have been obtained by utilizing reduced differential transform method and results have been compared through graphs and tables. Keywords: Time-fractional differential equations, Reduced differential transform methods, Murray equations, Caputo fractional derivative.

scholarly journals Solution of HIV and Malaria Coinfection Model Using Msgdtm

2015 ◽  
Vol 7 (4) ◽  
pp. 181
Author(s):  
Bonyah Ebenezer ◽  
Kwasi Awuah-Werekoh ◽  
Joseph Acquah
Keyword(s):  
Approximate Solution ◽  
Fractional Order ◽  
Epidemic Model ◽  
Unique Positive Solution ◽  
Transform Method ◽  
Order Form ◽  
Differential Transform ◽  
Infection Disease ◽  
Generalized Differential ◽  
Order Four

<p>In this paper, we investigate an epidemic model of HIV and Malaria co-infection using fractional order Calculus (FOC). The multistep generalized differential transform method (MSGDTM) is employed to obtain an accurate approximate solution to the epidemic model of HIV and Malaria co-infection disease in fractional order. A unique positive solution for HIV and Malaria co-infection is presented in fractional order form. For the integer case derivatives, the approximate solution of MSGDTM and the Runge–Kutta–order four scheme are compared. Numerical results are produced for the justification for this method.</p>

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 Analytical Study of Fractional-Order Multiple Chaotic FitzHugh-Nagumo Neurons Model Using Multistep Generalized Differential Transform Method

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Shaher Momani ◽  
Asad Freihat ◽  
Mohammed AL-Smadi
Keyword(s):  
Fractional Order ◽  
Fractional Derivatives ◽  
Analytical Study ◽  
Approximate Solutions ◽  
Differential Transform Method ◽  
Kutta Method ◽  
Transform Method ◽  
Runge Kutta Method ◽  
Differential Transform ◽  
Generalized Differential

The multistep generalized differential transform method is applied to solve the fractional-order multiple chaotic FitzHugh-Nagumo (FHN) neurons model. The algorithm is illustrated by studying the dynamics of three coupled chaotic FHN neurons equations with different gap junctions under external electrical stimulation. The fractional derivatives are described in the Caputo sense. Furthermore, we present figurative comparisons between the proposed scheme and the classical fourth-order Runge-Kutta method to demonstrate the accuracy and applicability of this method. The graphical results reveal that only few terms are required to deduce the approximate solutions which are found to be accurate and efficient.

Sign in / Sign up

Export Citation Format

Share Document