Approximate solution of Newell-Whitehead-Segel model with time-fractional derivative

Abstract

In the current analysis, we developed a significant approach for deriving the approximate solution of the Newell-Whitehead-Segel model with Caputo derivatives. This scheme is developed based on Sumudu transform and the residual power series method (RPSM) that generates the solution in the form of a series. First, we apply the Sumudu transform to decompose the fractional order and obtain a recurrence relation. Secondly, we utilize the RPSM to the recalescence relation and then we can derive the series solution with successive iterations using the initial conditions. We observe that this approach demonstrates a high accuracy and validity to the proposed fractional model. In our developed scheme, we do not face any huge calculation and restriction of elements that diverse the significance of the results. In addition, we display 2D and 3D graphical visuals to show the physical nature of the fractional model.

Solutions of a three-dimensional multi-term fractional anomalous solute transport model for contamination in groundwater

“…By encompassing non-integer orders, it extends conventional calculus, enabling the examination of intricate physical phenomena beyond the scope of integer-order models. This field finds practical utility in engineering and various applied sciences, including finance, electromagnetism, signal processing, control theory and mechanics [1][2][3][4][5][6][7][8]. The concept of fractional calculus allows the order of a partial differential equation to vary with respect to time or space.…”