Active Control of a Chaotic Fractional Order Economic System

This paper investigates the incompressible fractional MHD Maxwell fluid due to a power function accelerating plate with the first order slip, and the numerical analysis on the flow and heat transfer of fractional Maxwell fluid has been done. Moreover the deformation motion of fluid micelle is simply analyzed. Nonlinear velocity equation are formulated with multi-term time fractional derivatives in the boundary layer governing equations, and convective heat transfer boundary condition and viscous dissipation are both taken into consideration. A newly finite difference scheme with L1-algorithm of governing equations are constructed, whose convergence is confirmed by the comparison with analytical solution. Numerical solutions for velocity and temperature show the effects of pertinent parameters on flow and heat transfer of fractional Maxwell fluid. It reveals that the fractional derivative weakens the effects of motion and heat conduction. The larger the Nusselt number is, the greater the heat transfer capacity of fluid becomes, and the temperature gradient at the wall becomes more significantly. The lower Reynolds number enhances the viscosity of the fluid because it is the ratio of the viscous force and the inertia force, which resists the flow and heat transfer.

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“…And D α t is the Caputo fractional derivative operators and the definition of fractional derivative as follows (0 ≤ α ≤ 1): [37][38][39][40][41] …”

Section: Mathematical Formulationmentioning

confidence: 99%

Numerical analysis of fractional MHD Maxwell fluid with the effects of convection heat transfer condition and viscous dissipation

et al. 2017

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“…It would be interesting, for instance, to investigate possible q-extensions of the nonlinear Schroedinger equations advanced in [34,35]. Another venue of exploration that may be worth pursuing is to investigate q-extensions of nonlinear evolution equations involving fractional derivatives, such as those considered in [36][37][38].…”

Section: ∂S ∂Tmentioning

confidence: 99%

Nonlinear Wave Equations Related to Nonextensive Thermostatistics

Plastino

Wedemann

2017

Entropy

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Abstract:We advance two nonlinear wave equations related to the nonextensive thermostatistical formalism based upon the power-law nonadditive S q entropies. Our present contribution is in line with recent developments, where nonlinear extensions inspired on the q-thermostatistical formalism have been proposed for the Schroedinger, Klein-Gordon, and Dirac wave equations. These previously introduced equations share the interesting feature of admitting q-plane wave solutions. In contrast with these recent developments, one of the nonlinear wave equations that we propose exhibits real q-Gaussian solutions, and the other one admits exponential plane wave solutions modulated by a q-Gaussian. These q-Gaussians are q-exponentials whose arguments are quadratic functions of the space and time variables. The q-Gaussians are at the heart of nonextensive thermostatistics.The wave equations that we analyze in this work illustrate new possible dynamical scenarios leading to time-dependent q-Gaussians. One of the nonlinear wave equations considered here is a wave equation endowed with a nonlinear potential term, and can be regarded as a nonlinear Klein-Gordon equation. The other equation we study is a nonlinear Schroedinger-like equation.

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“…Thus, a lot of powerful methods, such as fractional linear multistep methods, variational iteration, galerkin finite element, Sumudu transform, trial equation, Adomian's decomposition, extended trial equation, homotopy analysis, iteration, homotopy perturbation, modified homotopy perturbation, generalized trigonometry functions, homotopy perturbation, Sumudu transform or modified trial equation method, have been presented in literature [2-17, 26-28, 30]. Besides these methods some authors have investigated various properties of fractional concepts [18,19,29,[32][33][34].…”

Section: Introductionmentioning

confidence: 99%

On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method

2015

Self Cite

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Abstract:In this paper, we apply the Fractional Adams-Bashforth-Moulton Method for obtaining the numerical solutions of some linear and nonlinear fractional ordinary differential equations. Then, we construct a table including numerical results for both fractional differential equations. Then, we draw two dimensional surfaces of numerical solutions and analytical solutions by considering the suitable values of parameters. Finally, we use the L 2 nodal norm and L 1 maximum nodal norm to evaluate the accuracy of method used in this paper.

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Active Control of a Chaotic Fractional Order Economic System

Cited by 136 publications

References 10 publications

Numerical analysis of fractional MHD Maxwell fluid with the effects of convection heat transfer condition and viscous dissipation

Numerical analysis of fractional MHD Maxwell fluid with the effects of convection heat transfer condition and viscous dissipation

Nonlinear Wave Equations Related to Nonextensive Thermostatistics

On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method

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