Abstract
In this paper, a recent and reliable method, named the fractional reduced differential transform method (FRDTM) is employed to solve one-dimensional time-fractional Beam equation subject to the appropriate initial conditions. This method provides the solutions very accurately and efficiently in convergent series form with easily computable coefficients. The efficacy and accuracy of this method are verified by means of three illustrative examples which indicate that the present method is very effective, simple, and easy to implement. Finally, it is observed that the FRDTM is the prevailing and convergent method for the solutions of linear and nonlinear fractional-order partial differential equations.
Highlights
In last few decades, fractional calculus has been attracted much attention due to its enormous numbers of applications in almost all disciplines of applied sciences and engineering
In the beginning of the twentieth century, researchers started to pay attention to find the robust and stable analytical approaches for the exact solution of the fractional differential equations [15]. Several schemes such as the Adomian decomposition methods [16,17,18], differential transform method [19,20,21], Homotopy perturbation method [22,23,24,25], Local fractional variation iteration method [26], Variation iteration method [27, 28], and Shifted Chebyshev polynomials based method [29] have been developed for the analytical solutions of fractional differential equations
The basic motivation of this paper is to propose fractional reduced differential transform method (FRDTM) to find an approximate analytical solution of the timefractional Beam equation given in (1)
Summary
Fractional calculus has been attracted much attention due to its enormous numbers of applications in almost all disciplines of applied sciences and engineering. Several schemes such as the Adomian decomposition methods [16,17,18], differential transform method [19,20,21], Homotopy perturbation method [22,23,24,25], Local fractional variation iteration method [26], Variation iteration method [27, 28], and Shifted Chebyshev polynomials based method [29] have been developed for the analytical solutions of fractional differential equations Most of these methods sometimes require complex and huge calculation in order to obtain approximate solutions.
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