Solving Time-Fractional Korteureg-de

In this paper, an analytic solution which has to do with the series expansion approach is proposed to determine the solution of time K-de V equation, specifically by FRDTM. The fractional derivatives are demonstrated in the Caputo sense. We compare the obtained results with R-K fourth order Method. It is possible to obtain solution closed to exact solution of a partial differential equation. To sum it up all, the accuracy, robustness, efficiency and convergence of this techniques are then illustrated through the numerical examples presented in this paper

Collage theorem-based approaches for solving inverse problems for differential equations : A review of recent developments

In this short survey, we review the current status of fractal-based techniques and their application to the solution of inverse problems for ordinary and partial differential equations. This involves an examination of several methods which are based on the so-called Collage Theorem, a simple consequence of Banach's Fixed Point Theorem, and its extensions

Fractional dynamical model for the generation of ECG like signals from filtered coupled Van-der Pol oscillators

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.In this paper, an incommensurate fractional order (FO) model has been proposed to generate ECG like waveforms. Earlier investigation of ECG like waveform generation is based on two identical Van-der Pol (VdP) family of oscillators, which are coupled by time delays and gains. In this paper, we suitably modify the three state equations corresponding to the nonlinear cross-product of states, time delay coupling of the two oscillators and low-pass filtering, using the concept of fractional derivatives. Our results show that a wide variety of ECG like waveforms can be simulated from the proposed generalized models, characterizing heart conditions under different physiological conditions. Such generalization of the modelling of ECG waveforms may be useful to understand the physiological process behind ECG signal generation in normal and abnormal heart conditions. Along with the proposed FO models, an optimization based approach is also presented to estimate the VdP oscillator parameters for representing a realistic ECG like signal.The work presented in this paper was supported by the E.U. ARTEMIS Joint Undertaking under the Cyclic and Person-Centric Health Management: Integrated appRoach for hOme, mobile and clinical eNvironments – (CHIRON) Project, Grant Agreement # 2009-1-100228

Novel techniques in parameter estimation for fractional dynamical models arising from biological systems

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Parameter- und Ordnungsidentifikation von fraktionalen Systemen mit einer Anwendung auf eine Lithium-Ionen-Batteriezelle

Model-based methods are increasingly being used for a safe and efficient operation of battery cells. For modeling battery cells, fractional models which are characterized by non-integer derivative orders have become established due to their electrochemical interpretability. In this work, methods for parameter and derivative order identification of fractional systems are derived without restriction with respect to the excitation at the begin of identification