An Attractive Approach Associated with Transform Functions for Solving Certain Fractional Swift-Hohenberg Equation
Date
8 NovemberMetadata
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Many phenomena in physics and engineering can be built by linear and nonlinear fractional partial differential equations which
are considered an accurate instrument to interpret these phenomena. In the current manuscript, the approximate analytical
solutions for linear and nonlinear time-fractional Swift-Hohenberg equations are created and studied by means of a recent
superb technique, named the Laplace residual power series (LRPS) technique under the time-Caputo fractional derivatives. The
proposed technique is a combination of the generalized Taylor’s formula and the Laplace transform operator, which depends
mainly on the concept of limit at infinity to find the unknown functions for the fractional series expansions in the Laplace
space with fewer computations and more accuracy comparing with the classical RPS that depends on the Caputo fractional
derivative for each step in obtaining the coefficient expansion. To test the simplicity, performance, and applicability of the
present method, three numerical problems of the time-fractional Swift-Hohenberg initial value problems are considered. The
impact of the fractional order β on the behavior of the approximate solutions at fixed bifurcation parameter is shown
graphically and numerically. Obtained results emphasized that the LRPS technique is an easy, efficient, and speed approach for
the exact description of the linear and nonlinear time-fractional models that arise in natural sciences.