The variational iteration method: An efficient scheme for handling fractional partial differential equations in fluid mechanics

By Zaid M. Odibat, Shaher Momani. Computers and Mathematics with Applications, 2009

315 citations recorded by the source corpus.

Citations in the corpus

Comparing the new fractional derivative operators involving exponential and Mittag-Leffler kernel (2020, unknown): “Consider the following well-known Burgers equation of fractional order [21] ∂u ∂tα + ∂u ∂x − ∂ (2)u ∂x2 = 2t2−α Γ (3− α) + 2(x− 1), t > 0, x ∈ R, 0 < α ≤ 1, (29)”
Alternative variational iteration method for solving the time-fractional Fornberg–Whitham equation (2015, unknown): “In [38], a general framework was presented for the VIM for fractional partial differential equations.”
The Variable-Order Fractional Calculus of Variations (2018, unknown): “We now apply our approximation techniques to the following one-dimensional linear inhomogeneous fractional Burgers’ equation of variable-order (see (Odibat and Momani, 2009, Example 5.2)): C 0 D α(t) t u(x, t) + ∂u ∂x (x, t)− ∂ 2u ∂x2 (x, t) = 2t2−α(t) Γ (3− α(t)) + 2x− 2, (3.11) for x ∈ [0, 1] and…”