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Solution of FPDE in Fluid Mechanics by ADM, VIM and NIM
American Journal of Mathematical and Computer Modelling
Volume 2, Issue 1, February 2017, Pages: 13-23
Received: Oct. 30, 2016; Accepted: Nov. 25, 2016; Published: Jan. 13, 2017
Authors
Khan Firdous, Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India
Khan Arshiya Anjum, Department of Computer Science and Information Technology, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India
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Abstract
By handling the one dimensional partial differential equation with three methods i.e. Adomain decomposition method(ADM), Variation iteration method(VIM) and the New iterative method(NIM) and applied logarithmic and exponential functions as initial condition. A general framework of these methods is presented for analytical treatment of fractional partial differential equation arises in fluid mechanics. The fractional derivatives are described in the Caputo sense. The equation used in this paper is fractional wave equation, fractional burgers equation and fractional Klein-Gordon equation. After comparison of the results, the series of solution are found which is very helpful. The basic idea described in this paper is accepted to be further in use to solve other similar linear problems in fractional calculus.
Keywords
Adomain Decomposition Method (ADM), Variation Iteration Method (VIM), New Iterative Method (NIM), Fractional Wave Equation, Fractional Burgers Equation, Fractional Klein-Gordon Equation
Kirtiwant Parshuram Ghadle, Khan Firdous, Khan Arshiya Anjum, Solution of FPDE in Fluid Mechanics by ADM, VIM and NIM, American Journal of Mathematical and Computer Modelling. Vol. 2, No. 1, 2017, pp. 13-23. doi: 10.11648/j.ajmcm.20170201.13
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