Journal
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume 43, Issue 4, Pages 1970-1987Publisher
WILEY
DOI: 10.1002/mma.6022
Keywords
Fractional differential equations; fractional Swift-Hohenberg equation; Laplace transform; q-Homotopy analysis transform method
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In this paper, the approximated analytical solution for fractional Swift-Hohenberg (S-H) equation is found with the aid of novel technique called q-homotopy analysis transform method (q-HATM). To ensure the applicability and efficiency of the proposed algorithm, we consider non-linear arbitrary-order S-H equation in presence and absence of dispersive term. The convergence analysis for the projected problem is presented, and the numerical simulations have been conducted to verify the future scheme is reliable and accurate. Further, the effect of bifurcation and dispersive parameters with physical importance on the probability density function for distinct fractional Brownian and standard motions are presented through plots. The obtained results elucidate that the proposed technique is easy to implement and very effective to analyse the complex problems that arose in science and technology.
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