Abstract
A novel approach to locate the approximate analytical solutions for non-linear partial differential equations is presented in this paper: the Yang transformation method combined with the Caputo derivative. In the current work, we determine the fractional Heat and Wave equation’s approximate analytical solutions. This current work addresses the Yang transformation approach in addition with the Caputo derivative. The suggested method yields approximately analytical solutions in the form of series with a simple, straightforward mechanics and a proportionality dependent on values of the fractional-order derivative. A few numerical heat equation and wave equation problems are solved to show the usefulness and reliability of the method. The tabular form [tables 7–12] makes the claim that the absolute error decreased as the number of terms in the series increased. It is also confirmed that the results are graphical compatible.
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