This paper deals with a ratio-dependent functional response predator-prey model with a fractional order derivative. The ratio-dependent models are very interesting, since they expose neither the paradox of enrichment nor the biological control paradox. We study the local stability of equilibria of the original system and its discretized counterpart. We show that the discretized system, which is...

In this study, the localfractional variational iterationmethod (LFVIM) and the localfractional series expansion method (LFSEM) are utilized to obtain approximate solutions for Korteweg-de Vries equation (KdVE) within local fractionalderivative operators (LFDOs). The efficiency of the considered methods is illustrated by some examples. The results reveal that the suggested algorithms are very ef...

The objective of our work is to couple the Elzaki transform method and local fractional derivative which called transform, where we have provided important results this transformation as Laplace-Elzaki duality, integral convolution, also presented properties some special functions with sense. was applied solve linear differential equations in order obtain non-differentiable analytical solutions...

and Applied Analysis 3 The nonlinear local fractional equation reads as L α u + N α u = 0, (19) where L α and N α are linear and nonlinear local fractional operators, respectively. Local fractional variational iteration algorithm can be written as [37] u n+1 (t) = u n (t) + t0 I t (α) {ξ α [L α u n (s) + N α u n (s)]} . (20) Here, we can construct a correction functional as follows [37]: u n+1 ...

In this article, the local fractional variational iteration method is proposed to solve nonlinear partial differential equations within local fractional derivative operators. To illustrate the ability and reliability of the method, some examples are illustrated. A comparison between local fractional variational iteration method with the other numerical methods is given, revealing that the propo...