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 work, firstly, some concepts of conformable fractional calculus in literature are given. Secondly, definitionsof ?-analytic point, ?-ordinary point and regular ? singular point are presented. Finally, the fractional 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?.

https://journalskuwait.org/kjs/index.php/KJS/article/download/1184/164

Solutions around a regular a singular point of a sequential conformable fractional differential equation

In this paper, we develop some modifications of the multiplic ative Newton method which are third-order convergence. We use the multiplicative Newton Theorem and Newton Cotes quad rature formulas to present these new modifications of the mul tiplicative Newton method. Using the multiplicative Taylor expansion, we give also the convergence analysis of these new methods. F urthermore, we compare the multiplicative Newton methods with the class ical Newton methods in details.

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Multiplicative Newton s Methods with Cubic Convergence

This paper investigates the accuracy of the differential transformation method (DTM) for solving the three-species food chain models which is described as three-dimensional system of ODES with quadratic and rational nonlinearities. Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. The direct symbolic-numeric scheme is indicated to be efficient and accurate.

	 

	Key words: Three-species food chain models, multi-step differential transformation method, attractors.

A numeric-analytic method for approximating three-species food chain models

In this work, we give the general solution sequential linear conformable fractional differential equations in the case of constant coefficients for {\alpha}(\in)(0,1]. In homogeneous case, we use a fractional exponential function which generalizes the corresponding ordinary function. In non-homogeneous case, we present to fractional the method of variation of parameters for a particular solution of sequential linear conformable fractional differential equations.

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General Solution to Sequential Linear Conformable Fractional Differential Equations With Constant Coefficients

Abstract In this paper, the approximate solution of delay differential equations is obtained by a reliable algorithm based on an adaptation of the classical variational iteration method (VIM), which is called the multi-stage variational iteration method (MSVIM). Examples are carried out and numerical results with comparison to exact solutions, VIM and MATLAB dde23 solver are given. The comparison reveals that the MSVIM is a promising tool to solve delay differential equations.

Ahmet Gökdoğan

Papers

Solutions around a regular a singular point of a sequential conformable fractional differential equation

Multiplicative Newton s Methods with Cubic Convergence

A numeric-analytic method for approximating three-species food chain models

General Solution to Sequential Linear Conformable Fractional Differential Equations With Constant Coefficients

A Multistage Variational Iteration Method for Solution of Delay Differential Equations