Nature often presents complex dynamics, which cannot be explained by means of ordinary models. In this paper, we establish an approach to certain fractional dynamic systems using only deterministic arguments. The behavior of the trajectories of fractional non-linear autonomous systems around the corresponding critical points in the phase space is studied. In this work we arrive to several inter...

In some real world problems, fractional-order models are found to be more adequate than integer-order models. Fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various materials and processes. The mathematical modelling of systems and processes in the fields of physics, chemistry, aerodynamics, electro dynamics of complex medium, polymer...

in this paper, under appropriate oscillating behaviours of the nonlinear term, we prove some multiplicity results for a class of nonlinear fractional equations. these problems have a variational structure and we find three solutions for them by exploiting an abstract result for smooth functionals defined on a reflexive banach space. to make the nonlinear methods work, some careful analysis of t...

‎ in this paper, we investigate stability analysis of fractional differential systems equipped with the conformable fractional derivatives. some stability conditions of fractional differential systems are proposed by applying the fractional exponential function and the fractional laplace transform. moreover, we check the stability of conformable fractional lotka-volterra system with the multi-st...

This paper is concerned with the numerical solutions of a variable-order space-time fractional reaction-diffusion model. The space-time fractional derivative is considered in the sense of Riesz-Feller, the system is defined by replacing the second order space derivatives with the variable Riesz-Feller derivatives. The problem is solved by an explicit finite difference method. Finally, simulatio...

In this article, we show that Laplace transform can be applied to fractional system. To this end, solutions of linear fractional-order equations are first derived by a direct method, without using Laplace transform. Then the solutions of fractional-order differential equations are estimated by employing Gronwall and Hölder inequalities. They are showed be to of exponential order, which are nece...

One-dimensional Ginzburg–Landau equations with derivatives of noninteger order are considered. Using psi-series with fractional powers, the solution of the fractional Ginzburg–Landau (FGL) equation is derived. The leading-order behaviours of solutions about an arbitrary singularity, as well as their resonance structures, have been obtained. It was proved that fractional equations of order α wit...

Discrete-time fractional derivative filters (1-D and 2-D) are shown to be well approximated from a small set of integer derivatives. A fractional derivative of arbitrary order (and, in 2-D, of arbitrary orientation) can therefore be efficiently computed from a linear combination of integer derivatives of the underlying signal or image.