An efficient method for the analytical study of linear and nonlinear time-fractional partial differential equations with variable coefficientsстатьяИсследовательская статья
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Дата последнего поиска статьи во внешних источниках: 15 февраля 2024 г.
Аннотация:The residual power series method is effective for obtaining approximateanalytical solutions to fractional-order differential equations. This method,however, requires the derivative to compute the coefficients of terms in aseries solution. Other well-known methods, such as the homotopy perturbation, the Adomian decomposition, and the variational iteration methods,need integration. We are all aware of how difficult it is to calculate the fractional derivative and integration of a function. As a result, the use of themethods mentioned above is somewhat constrained. In this research work,approximate and exact analytical solutions to time-fractional partial differential equations with variable coefficients are obtained using the Laplaceresidual power series method in the sense of the Gerasimov–Caputo fractional derivative. This method helped us overcome the limitations of thevarious methods. The Laplace residual power series method performs exceptionally well in computing the coefficients of terms in a series solution byapplying the straightforward limit principle at infinity, and it is also more effective than various series solution methods due to the avoidance of Adomia and He polynomials to solve nonlinear problems. The relative, recurrence,and absolute errors of the three problems are investigated in order to evaluate the validity of our method. The results show that the proposed methodcan be a suitable alternative to the various series solution methods whensolving time-fractional partial differential equations.