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

Coullet sistemi olarak bilinen nonlineer denklem sisteminin cozumu diferensiyel donusum yontemi ile elde edildi. Sayisal sonuclar, onerilen yontemin etkinligini ve dogrulugunu gostermek icin dorduncu mertebeden Runge-Kutta yontemi ile karsilastirildi. Onerilen yontemin guclu, dogru ve kolayca uygulanabilirligi gosterildi.

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On Solving Coullet System by Differential Transformation Method

3 Abstract: In this article, homotopy perturbation method coupled with Laplace transform and Pade 0approximants is applied on the re-formulated nonlinear oscillatory systems. Numerical results and graphical represenations explicitly reveal the complete reliability and effeicincy of the suggested algorithm.

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Coupling of Homotopy Perturbation, Laplace Transform and Padé Approximants for Nonlinear Oscillatory Systems

In this article, trigonometric curve fitting on the multi-step differential transformation method (MsDTM) is implemented to give approximate analytical solutions of nonlinear ordinary differential equation such as non-linear oscillation systems. In addition, the solution obtained from MsDTM applied trigonometric curve fitting. Our proposed approach reveals that results to approximate analytical solutions of non-linear oscillation systems . Some plots are presented to show the reliability and simplicity of the methods.

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Trigonometric Curve Fitting Based on Multi-step Differential Transformation Method and the Application of Non-linear Oscillatory Systems

The effects of stacking sequences of composite laminated optical beams on free vibration frequencies are investigated using two methods: the Boubaker Polynomials Expansion Scheme (pbes) and the Differential Quadrature Method (dqm). In the last decades, these two techniques have been separately performed for obtaining accurate numerical solutions to several initial boundary value problems (Vo et al. 2010, Li et al. 2008, Chen 2003, Hu et al. 2008, Karami et al. 2003, Malekzadeh et al. 2004, Khare et al. 2004, Della and Shu 2005, Ramtekkar et al. 2002, Adam 2003). Conjointly yielded results are compared and discussed.

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Comparative Analysis of Free Optical Vibration of Lamination Composite Optical Beams Using the Boubaker Polynomials Expansion Scheme and the Differential Quadrature Method

Ahmet Gökdoğan

Papers

On Solving Coullet System by Differential Transformation Method

Coupling of Homotopy Perturbation, Laplace Transform and Padé Approximants for Nonlinear Oscillatory Systems

Trigonometric Curve Fitting Based on Multi-step Differential Transformation Method and the Application of Non-linear Oscillatory Systems

Comparative Analysis of Free Optical Vibration of Lamination Composite Optical Beams Using the Boubaker Polynomials Expansion Scheme and the Differential Quadrature Method