scholarly journals Approximate and generalized solutions of conformable type Coudrey–Dodd–Gibbon–Sawada–Kotera equation

2020 ◽  
pp. 2150021
Author(s):  
Mehmet Senol ◽  
Lanre Akinyemi ◽  
Ayşe Ata ◽  
Olaniyi S. Iyiola
Keyword(s):  
Fractional Order ◽  
Approximate Solutions ◽  
Generalized Solutions ◽  
Analysis Method ◽  
Approximate Methods ◽  
Power Series Method ◽  
Closed Form Solutions ◽  
Homotopy Analysis ◽  
Residual Power Series ◽  
Residual Power

In this study, we consider conformable type Coudrey–Dodd–Gibbon–Sawada–Kotera (CDGSK) equation. Three powerful analytical methods are employed to obtain generalized solutions of the nonlinear equation of interest. First, the sub-equation method is used as baseline where generalized closed form solutions are obtained and are exact for any fractional order [Formula: see text]. Furthermore, residual power series method (RPSM) and [Formula: see text]-homotopy analysis method ([Formula: see text]-HAM) are then applied to obtain approximate solutions. These are possible using some properties of conformable derivative. These approximate methods are very powerful and efficient due to the absence of the need for linearization, discretization and perturbation. Numerical simulations are carried out showing error values, [Formula: see text]-curve for [Formula: see text]-HAM and the effects of fractional order on the solution profiles.

scholarly journals Efficient analytical techniques for solving time-fractional nonlinear coupled Jaulent–Miodek system with energy-dependent Schrödinger potential

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Mehmet Şenol ◽  
Olaniyi S. Iyiola ◽  
Hamed Daei Kasmaei ◽  
Lanre Akinyemi
Keyword(s):  
Analytical Techniques ◽  
Convergent Series ◽  
Analysis Method ◽  
Power Series Method ◽  
Strongly Nonlinear ◽  
Homotopy Analysis ◽  
Residual Power Series ◽  
Fractional Differential ◽  
Energy Dependent ◽  
Residual Power

Abstract In this paper, we present analytical-approximate solution to the time-fractional nonlinear coupled Jaulent–Miodek system of equations which comes with an energy-dependent Schrödinger potential by means of a residual power series method (RSPM) and a q-homotopy analysis method (q-HAM). These methods produce convergent series solutions with easily computable components. Using a specific example, a comparison analysis is done between these methods and the exact solution. The numerical results show that present methods are competitive, powerful, reliable, and easy to implement for strongly nonlinear fractional differential equations.

scholarly journals Application of Residual Power Series Method to Fractional Coupled Physical Equations Arising in Fluids Flow

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Anas Arafa ◽  
Ghada Elmahdy
Keyword(s):  
Power Series ◽  
Power Efficiency ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Series Method ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Homotopy Analysis ◽  
Residual Power Series ◽  
Residual Power

The approximate analytical solution of the fractional Cahn-Hilliard and Gardner equations has been acquired successfully via residual power series method (RPSM). The approximate solutions obtained by RPSM are compared with the exact solutions as well as the solutions obtained by homotopy perturbation method (HPM) and q-homotopy analysis method (q-HAM). Numerical results are known through different graphs and tables. The fractional derivatives are described in the Caputo sense. The results light the power, efficiency, simplicity, and reliability of the proposed method.

scholarly journals Approximate Solutions of Two-Dimensional Burgers' and Coupled Burgers' Equations by Residual Power Series Method

2018 ◽  
Vol 22 ◽  
pp. 01044
Author(s):  
Selahattin Gulsen ◽  
Mustafa Inc ◽  
Harivan R. Nabi
Keyword(s):  
Power Series ◽  
Taylor Series Expansion ◽  
Approximate Solutions ◽  
Two Dimensional ◽  
Series Method ◽  
Power Series Method ◽  
Burgers Equations ◽  
Residual Power Series Method ◽  
Residual Power Series ◽  
Residual Power

In this study, two-dimensional Burgers' and coupled Burgers' equations are examined by the residual power series method. This method provides series solutions which are rapidly convergent and their components are easily calculable by Mathematica. When the solution is polynomial, the method gives the exact solution using Taylor series expansion. The results display that the method is more efficient, applicable and accuracy and the graphical consequences clearly present the reliability of the method.

scholarly journals Fractional residual power series method for the analytical and approximate studies of fractional physical phenomena

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 799-805
Author(s):  
Gamal Mohamed Ismail ◽  
Hamdy Ragab Abdl-Rahim ◽  
Hijaz Ahmad ◽  
Yu-Ming Chu
Keyword(s):  
Power Series ◽  
Fractional Derivatives ◽  
Approximate Solutions ◽  
Series Method ◽  
Fractional Partial Differential Equation ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Residual Power Series ◽  
Physical Phenomena ◽  
Residual Power

AbstractIn this article, analytical exact and approximate solutions for fractional physical equations are obtained successfully via efficient analytical method called fractional residual power series method (FRPSM). The fractional derivatives are described in the Caputo sense. Three applications are discussed, showing the validity, accuracy and efficiency of the present method. The solution via FRPSM shows excellent agreement in comparison with the solutions obtained from other established methods. Also, the FRPSM can be used to solve other nonlinear fractional partial differential equation problems. The final results are presented in graphs and tables, which show the effectiveness, quality and strength of the presented method.

scholarly journals Approximate solutions and conservation laws of the periodic base temperature of convective longitudinal fins in thermal conductivity

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 267-273
Author(s):  
Isa Aliyu ◽  
Mustafa Inc ◽  
Abdullahi Yusuf ◽  
Dumitru Baleanu
Keyword(s):  
Thermal Conductivity ◽  
Power Series ◽  
Linear Models ◽  
Approximate Solutions ◽  
Base Temperature ◽  
Series Method ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Residual Power Series ◽  
Residual Power

In this paper, the residual power series method is used to study the numerical approximations of a model of oscillating base temperature processes occurring in a convective rectangular fin with variable thermal conductivity. It is shown that the residual power series method is efficient for examining numerical behavior of non-linear models. Further, the conservation of heat is studied using the multiplier method.

scholarly journals Residual power series method for solving nonlinear reaction-diffusion-convection problems

2021 ◽  
Vol 39 (3) ◽  
pp. 177-188
Author(s):  
Maisa Khader ◽  
Mahmoud H. DarAssi
Keyword(s):  
Power Series ◽  
Reaction Diffusion ◽  
Approximate Solutions ◽  
Series Method ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Nonlinear Reaction ◽  
Residual Power Series ◽  
Diffusion Convection ◽  
Residual Power

In this paper, the residual power series method (RPSM) is applied to one of the most frequently used models in engineering and science, a nonlinear reaction diffusion convection initial value problems. The approximate solutions using the RPSM were compared to the exact solutions and to the approximate solutions using the homotopy analysis method.

scholarly journals Residual Power Series Method for Solving Klein-Gordon Schrödinger Equation

2021 ◽  
Vol 9 (2) ◽  
pp. 123-127
Author(s):  
Ssaad A. Manaa ◽  
Fadhil H. Easif ◽  
Jomaa J. Murad
Keyword(s):  
Power Series ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Approximate Solutions ◽  
Series Method ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Residual Power Series ◽  
Klein Gordon ◽  
Residual Power

In this work, the   Residual Power Series Method(RPSM) is used to find the approximate solutions of Klein Gordon Schrödinger (KGS) Equation. Furthermore, to show the accuracy and the efficiency of the presented method, we compare the obtained approximate solution of Klein Gordon Schrödinger equation by Residual Power Series Method(RPSM) numerically and graphically with the exact solution.

scholarly journals The Analysis of Fractional-Order Navier-Stokes Model Arising in the Unsteady Flow of a Viscous Fluid via Shehu Transform

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Pongsakorn Sunthrayuth ◽  
Rasool Shah ◽  
A. M. Zidan ◽  
Shahbaz Khan ◽  
Jeevan Kafle
Keyword(s):  
Fractional Order ◽  
Fractional Derivatives ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Navier Stokes ◽  
Power Series Method ◽  
Navier Stokes Equations ◽  
Residual Power Series ◽  
Residual Power

This paper presents a new method that is constructed by combining the Shehu transform and the residual power series method. Precisely, we provide the application of the proposed technique to investigate fractional-order linear and nonlinear problems. Then, we implemented this new technique to obtain the result of fractional-order Navier-Stokes equations. Finally, we provide three-dimensional figures to help the effect of fractional derivatives on the actions of the achieved profile results on the proposed models.

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