Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks

In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Laplace and Fourier transforms are analyzed and the results for the anomalous diffusion equations of variable order are discussed. The new formulation is efficient in modeling a class of concentrations in the complex transport process.

A new fractional operator of variable order: Application in the description of anomalous diffusion

The aim of this article is to propose a new definition of fuzzy fractional derivative, so-called fuzzy conformable. To this end, we discussed fuzzy conformable fractional integral softly. Meanwhile, uniqueness, existence, and other properties of solutions of certain fuzzy conformable fractional differential equations under strongly generalized differentiability are also utilized. Furthermore, all needed requirements for characterizing solutions by equivalent systems of crisp conformable fractional differential equations are debated. In this orientation, modern trend and new computational algorithm in terms of analytic and approximate conformable solutions are proposed. Finally, the reproducing kernel Hilbert space method in the conformable emotion is constructed side by side with numerical results, tabulated data, and graphical representations.

Fuzzy conformable fractional differential equations: novel extended approach and new numerical solutions

Fractional-order neural networks play a vital role in modeling the information processing of neuronal interactions. It is still an open and necessary topic for fractional-order neural networks to investigate their global stability. This paper proposes some simplified linear matrix inequality (LMI) stability conditions for fractional-order linear and nonlinear systems. Then, the global stability analysis of fractional-order neural networks employs the results from the obtained LMI conditions. In the LMI form, the obtained results include the existence and uniqueness of equilibrium point and its global stability, which simplify and extend some previous work on the stability analysis of the fractional-order neural networks. Moreover, a generalized projective synchronization method between such neural systems is given, along with its corresponding LMI condition. Finally, two numerical examples are provided to illustrate the effectiveness of the established LMI conditions.

LMI Conditions for Global Stability of Fractional-Order Neural Networks

Solution of conformable fractional ordinary differential equations via differential transform method

In this article, a variational iteration method (VIM) is performed to give approximate and analytical solutions of nonlinear ordinary differential equation systems such as a model for HIV infection of CD4 +  T cells. A modified VIM (MVIM), based on the use of Pade approximants is proposed. Some plots are presented to show the reliability and simplicity of the methods.

Ahmet Gökdoğan

Papers

Solution of conformable fractional ordinary differential equations via differential transform method

On the numerical solution of the model for HIV infection of CD4+ T cells

The modified algorithm for the differential transform method to solution of Genesio systems

A multistage differential transformation method for approximate solution of Hantavirus infection model

Adaptive multi-step differential transformation method to solving nonlinear differential equations