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 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.

Application of He’s Homotopy Perturbation Method for Solving Fractional Fokker-Planck Equations

2009 ◽  
Vol 64 (12) ◽  
pp. 788-794 ◽  
Author(s):  
Mohamed M. Mousa ◽  
Aidarkhan Kaltayev
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Planck Equation ◽  
Approximate Solutions ◽  
Convergent Series ◽  
Homotopy Perturbation ◽  
External Force Field ◽  
Promising Tool ◽  
Transport Problems ◽  
Fokker Planck

Abstract The fractional Fokker-Planck equation (FFPE) has been used in many physical transport problems which take place under the influence of an external force field and other important applications in various areas of engineering and physics. In this paper, by means of the homotopy perturbation method (HPM), exact and approximate solutions are obtained for two classes of the FFPE initial value problems. The method gives an analytic solution in the form of a convergent series with easily computed components. The obtained results show that the HPM is easy to implement, accurate and reliable for solving FFPEs. The method introduces a promising tool for solving other types of differential equation with fractional order derivatives

scholarly journals Homotopy Perturbation Method for Fractional Gas Dynamics Equation Using Sumudu Transform

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Jagdev Singh ◽  
Devendra Kumar ◽  
A. Kılıçman
Keyword(s):  
Perturbation Method ◽  
Gas Dynamics ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Adomian Decomposition Method ◽  
Homotopy Perturbation ◽  
He’S Polynomials ◽  
Adomian Decomposition ◽  
Sumudu Transform ◽  
Gas Dynamics Equation

A user friendly algorithm based on new homotopy perturbation Sumudu transform method (HPSTM) is proposed to solve nonlinear fractional gas dynamics equation. The fractional derivative is considered in the Caputo sense. Further, the same problem is solved by Adomian decomposition method (ADM). The results obtained by the two methods are in agreement and hence this technique may be considered an alternative and efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations. The 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. The numerical solutions obtained by the proposed method show that the approach is easy to implement and computationally very attractive.

scholarly journals An Efficient Approach for Fractional Harry Dym Equation by Using Sumudu Transform

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Devendra Kumar ◽  
Jagdev Singh ◽  
A. Kılıçman
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Efficient Approach ◽  
Homotopy Perturbation ◽  
He’S Polynomials ◽  
Adomian Decomposition ◽  
Sumudu Transform ◽  
Dym Equation ◽  
Harry Dym Equation

An efficient approach based on homotopy perturbation method by using sumudu transform is proposed to solve nonlinear fractional Harry Dym equation. This method is called homotopy perturbation sumudu transform (HPSTM). Furthermore, the same problem is solved by Adomian decomposition method (ADM). The results obtained by the two methods are in agreement, and, hence, this technique may be considered an alternative and efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations. The 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. The numerical solutions obtained by the HPSTM show that the approach is easy to implement and computationally very attractive.

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