scholarly journals Homotopy perturbation method with Laplace Transform (LT-HPM) for solving Lane–Emden type differential equations (LETDEs)

SpringerPlus ◽  
2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Rajnee Tripathi ◽  
Hradyesh Kumar Mishra
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation

scholarly journals Analysis of Homotopy Perturbation Method for Solving Fractional Order Differential Equations

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 40 ◽  
Author(s):  
Shumaila Javeed ◽  
Dumitru Baleanu ◽  
Asif Waheed ◽  
Mansoor Shaukat Khan ◽  
Hira Affan
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Fractional Order ◽  
Homotopy Perturbation Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Fractional Order Differential Equations ◽  
Homotopy Perturbation ◽  
The Given ◽  
Ordinary Derivative

The analysis of Homotopy Perturbation Method (HPM) for the solution of fractional partial differential equations (FPDEs) is presented. A unified convergence theorem is given. In order to validate the theory, the solution of fractional-order Burger-Poisson (FBP) equation is obtained. Furthermore, this work presents the method to find the solution of FPDEs, while the same partial differential equation (PDE) with ordinary derivative i.e., for α = 1 , is not defined in the given domain. Moreover, HPM is applied to a complicated obstacle boundary value problem (BVP) of fractional order.

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