Laplace transform and fractional differential equations

Li, Kexue; Peng, Jigen

doi:10.1016/j.aml.2011.05.035

Cited by 222 publications

(77 citation statements)

References 6 publications

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“…We intend to show that the field of applications of the Sumudu can be extended much further, as was declared in ( Belgacem [6]). In fact, we will follow in the footsteps of Kuexe and Jigen [20], who in their recent work have formulated a rational for applying the Laplace transform to FDE's. The thrust of our present work is to establish a simple yet a robust scheme for applying the Sumudu to FDE's.…”

Section: Introductionmentioning

confidence: 98%

Solving special fractional differential equations by Sumudu transform

Goswami

Belgacem

2012

AIP Conference Proceedings

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Study of nonlinear ohmic heating and ponderomotive force effects on the self-focusing and defocusing of Gaussian laser beams in collisional underdense plasmas Phys. Plasmas 19, 113107 (2012) Blow-up criteria of solutions for a modified two-component hyperelastic rod system J. Math. Phys. 53, 123501 (2012) Disorder-induced dynamics in a pair of coupled heterogeneous phase oscillator networks Chaos 22, 043104 (2012) Attractiveness of periodic orbits in parametrically forced systems with time-increasing friction J. Math. Phys. 53, 102703 (2012) Long-time behavior of a two-layer model of baroclinic quasi-geostrophic turbulence Abstract. In the present paper, we give a sufficient condition to guarantee the solution of the constant coefficient fractional differential equation by the Sumudu transform.

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Section: Introductionmentioning

confidence: 98%

Solving special fractional differential equations by Sumudu transform

Goswami

Belgacem

2012

AIP Conference Proceedings

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“…In this section we give some basic definitions and properties of fractional operators, the special function and the solution representation of fractional integrodifferential equations (Kexue and Jigen, 2011;Kilbas et al, 2006;Miller and Ross, 1993;Oldham and Spanier, 1974;Podlubny, 1999;Samko et al, 1993;Kaczorek, 2011).…”

Section: Preliminariesmentioning

confidence: 99%

Controllability of nonlinear implicit fractional integrodifferential systems

Balachandran

Divya

2014

International Journal of Applied Mathematics and Computer Science

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“…of α-th derivative (α ∈ R + ) can also be used to describe a fractional systems [37,38]. With both the input signal u(t) and the output signal y(t) equal to 0 for all t < 0, allows Equation (1) to be written in a transfer function form…”

Section: Fractional Differential System Equationmentioning

confidence: 99%

“…It should be noted that the models given in Equations (35) and (36) may not be suitable for simulation, as parameters are optimized for prediction. Instead, the predictors in Equations (37) and (38) should be used for 1-step-ahead power delivery/storage prediction of the battery. As shown in Figure 8, the comparison of the predicted and measured results indicates that the estimated voltage and curent FDMs obtained via the LSSVF method can both capture the dynamics of the voltage and current signals of the battery system.…”

Section: Experimental Data-based Modelingmentioning

confidence: 99%

Dynamic Prediction of Power Storage and Delivery by Data-Based Fractional Differential Models of a Lithium Iron Phosphate Battery

et al. 2016

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A fractional derivative system identification approach for modeling battery dynamics is presented in this paper, where fractional derivatives are applied to approximate non-linear dynamic behavior of a battery system. The least squares-based state-variable filter (LSSVF) method commonly used in the identification of continuous-time models is extended to allow the estimation of fractional derivative coefficents and parameters of the battery models by monitoring a charge/discharge demand signal and a power storage/delivery signal. In particular, the model is combined by individual fractional differential models (FDMs), where the parameters can be estimated by a least-squares algorithm. Based on experimental data, it is illustrated how the fractional derivative model can be utilized to predict the dynamics of the energy storage and delivery of a lithium iron phosphate battery (LiFePO 4 ) in real-time. The results indicate that a FDM can accurately capture the dynamics of the energy storage and delivery of the battery over a large operating range of the battery. It is also shown that the fractional derivative model exhibits improvements on prediction performance compared to standard integer derivative model, which in beneficial for a battery management system. Keywords: fractional differential model (FDM); energy storage and delivery; system identification; battery management system (BMS); least squares-based state-variable filter (LSSVF) method

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Laplace transform and fractional differential equations

Cited by 222 publications

References 6 publications

Solving special fractional differential equations by Sumudu transform

Solving special fractional differential equations by Sumudu transform

Controllability of nonlinear implicit fractional integrodifferential systems

Dynamic Prediction of Power Storage and Delivery by Data-Based Fractional Differential Models of a Lithium Iron Phosphate Battery

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