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Analytical approach to linear fractional partial differential equations arising in fluid mechanics. (English) Zbl 1378.76084
Summary: In this letter, we implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving linear fractional partial differential equations arising in fluid mechanics. The fractional derivatives are described in the Caputo sense. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these methods, the solution takes the form of a convergent series with easily computable components. The corresponding solutions of the integer order equations are found to follow as special cases of those of fractional order equations. Some numerical examples are presented to illustrate the efficiency and reliability of the two methods.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35R11 Fractional partial differential equations
35Q35 PDEs in connection with fluid mechanics
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