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 paper, the approximate solution of the differential system modeling HIV infection of CD4+ T cells isobtained by a reliable algorithm based on an adaptation of the standard variational iteration method (VIM), which is called the multi-stage variational iteration method(MSVIM). A comparison between MSVIM and the fourthorder Runge-Kutta method (RK4-method) reveal that the proposed technique is a promising tool to solve the considered problem.

http://ijsts.shirazu.ac.ir/pdf_2123_685164b820c6583e2a0af41b665cf44f.html

An approximate solution of a model for HIV infection of CD4+ T cells

In this work, the power series solutions are given around a regular-singular point, in the case of variable coefficients for homogeneous sequential linear conformable fractional differential equations of order 2{\alpha}.

Solutions around a Regular {\alpha} Singular Point of a Sequential Conformable Fractional Differential Equation

In this work, we study the fractional power series solutions around regular singular point x=0 of conformable fractional Bessel differential equation and fractional Bessel functions. Then, we compare fractional solutions with ordinary solutions. In addition, we present certain property of fractional Bessel functions.

Conformable Fractional Bessel Equation and Bessel Functions

An approximate analytical solution in the form of a rapidly convergent series for tracing light rays through an inhomogeneous graded index medium is developed, using the multi-step differential transform method based on the classical differential transformation method. Numerical results are compared to those obtained by the fourth-order Runge—Kutta method to illustrate the precision and effectiveness of the proposed method. Results are given in explicit and graphical forms.

Numerical Approximations to the Solution of Ray Tracing through the Crystalline Lens

In this paper, it is given a fast algorithm to solve chaotic differential systems using the multi-step differential transforms method (MsDTM) The approach is applied to a number of chaotic nonlinear differential equations and numerical results are given Performance analyses reveal that the proposed approach is an efficiency tool to solve using fewer time step to the considered equation systems

https://journalskuwait.org/kjs/index.php/KJS/article/download/81/12

Ahmet Gökdoğan

Papers

An approximate solution of a model for HIV infection of CD4+ T cells

Solutions around a Regular {\alpha} Singular Point of a Sequential Conformable Fractional Differential Equation

Conformable Fractional Bessel Equation and Bessel Functions

Numerical Approximations to the Solution of Ray Tracing through the Crystalline Lens

Adaptive multi-step differential transformation method to solve ODE systems