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

Baskonus, Hacı Mehmet; Bulut, Hasan

doi:10.1515/math-2015-0052

Cited by 117 publications

(60 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are two types of Adams methods, the Adams-Bashforth and the Adams-Moulton. The combination of these methods results in the predictor-corrector Adams-Bashforth-Moulton Method [23][24][25][26].…”

Section: Fractional Operatorsmentioning

confidence: 99%

Bateman–Feshbach Tikochinsky and Caldirola–Kanai Oscillators with New Fractional Differentiation

Coronel‐Escamilla

Gómez-Aguilar

Băleanu

et al. 2017

Entropy

View full text Add to dashboard Cite

Abstract:In this work, the study of the fractional behavior of the Bateman-Feshbach-Tikochinsky and Caldirola-Kanai oscillators by using different fractional derivatives is presented. We obtained the Euler-Lagrange and the Hamiltonian formalisms in order to represent the dynamic models based on the Liouville-Caputo, Caputo-Fabrizio-Caputo and the new fractional derivative based on the Mittag-Leffler kernel with arbitrary order α. Simulation results are presented in order to show the fractional behavior of the oscillators, and the classical behavior is recovered when α is equal to 1.

show abstract

Section: Fractional Operatorsmentioning

confidence: 99%

Bateman–Feshbach Tikochinsky and Caldirola–Kanai Oscillators with New Fractional Differentiation

Coronel‐Escamilla

Gómez-Aguilar

Băleanu

et al. 2017

Entropy

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

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

Cited by 117 publications

References 17 publications

Bateman–Feshbach Tikochinsky and Caldirola–Kanai Oscillators with New Fractional Differentiation

Bateman–Feshbach Tikochinsky and Caldirola–Kanai Oscillators with New Fractional Differentiation

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

Contact Info

Product

Resources

About