• FODE

  • Referenced in 296 articles [sw08377]
  • transformed into a time fractional ordinary differential equation (FODE) in the sense of Caputo derivative ... discretizing classical Fokker-Planck equation, some numerical results for time fractional Fokker-Planck equation with...
  • Mittag-Leffler

  • Referenced in 89 articles [sw12626]
  • appears frequently in solutions of fractional differential equations (i.e. differential equations containing fractional derivatives...
  • FracPECE

  • Referenced in 73 articles [sw24209]
  • numerical solution of differential equations of fractional order. We present and discuss an algorithm ... numerical solution of nonlinear differential equations of fractional (i.e., non-integer) order. This algorithm allows ... materials. The model contains a nonlinear differential equation of order β, where...
  • mlf

  • Referenced in 57 articles [sw18400]
  • appears frequently in solutions of fractional differential equations (i.e. differential equations containing fractional derivatives). USAGE...
  • FracSym

  • Referenced in 28 articles [sw16769]
  • symbolic computation of Lie symmetries of fractional differential equations. In this paper, we present ... point symmetries for fractional order differential equations (FDEs) using the method as described ... Continuous transformation groups of fractional differential equations”, Vestn. USATU...
  • DeepXDE

  • Referenced in 38 articles [sw32456]
  • different types of PDEs, including integro-differential equations, fractional PDEs, and stochastic PDEs. Moreover, from...
  • FOTF Toolbox

  • Referenced in 21 articles [sw19507]
  • provided for fractional derivatives and fractional differential equations; (2) Two classes, FOTF and FOSS ... modelling, analysis and design of multivariable fractional-order systems...
  • Maxima

  • Referenced in 169 articles [sw00560]
  • series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors ... high precision numeric results by using exact fractions, arbitrary precision integers, and variable precision floating...
  • FDE12

  • Referenced in 10 articles [sw22502]
  • Predictor-corrector PECE method for fractional differential equations. MATLAB Central File Exchange. FDE12 solves ... problem for a non-linear differential equation of fractional order (FDE). This is an implementation...
  • YUIMA

  • Referenced in 45 articles [sw11399]
  • discretely observed fractional Ornstein-Uhlenbeck process solution of the stochastic differential equation ... fractional Brownian motion. For the estimation of the drift λ, the results are obtained only...
  • SENKIN

  • Referenced in 22 articles [sw12845]
  • species mass fractions and the set of linear differential equations that describe the first-order...
  • ADMP

  • Referenced in 6 articles [sw10220]
  • analytic approximate solutions for nonlinear fractional differential equations. The Adomian decomposition method ... construct analytic approximate solutions for nonlinear differential equations. In this paper, based ... construct analytic approximate solutions for nonlinear fractional differential equations with initial or boundary conditions. Furthermore...
  • averaging

  • Referenced in 4 articles [sw38869]
  • averaging principle for fractional stochastic differential equations with Lévy noise. This paper is devoted ... averaging principle for fractional stochastic differential equations in (mathbb{R}^n) with Lévy motion, using ... equation under suitable assumptions. Furthermore, we show that the solutions of the averaged equation approach ... original equation. Our results provide a better understanding for effective approximation of fractional dynamical systems...
  • FPINNs

  • Referenced in 27 articles [sw40570]
  • fPINNs: Fractional Physics-Informed Neural Networks. Physics-informed neural networks (PINNs ... effective in solving integer-order partial differential equations (PDEs) based on scattered and noisy data ... explicitly encoded into the NN using automatic differentiation, while the sum of the mean-squared ... PINNs to fractional PINNs (fPINNs) to solve space-time fractional advection-diffusion equations (fractional ADEs...
  • Kernel compression

  • Referenced in 1 article [sw22517]
  • Kernel compression time stepping schemes for fractional differential equations. High-order accurate, adaptive, kernel compression ... schemes for fractional differential equations. An implementation of efficient and accurate kernel compression time-stepping ... schemes for the adaptive solution of fractional differential equations. The schemes are high order accurate...
  • MTIEU1

  • Referenced in 11 articles [sw01232]
  • eigenvalues and eigenfunctions of Mathieu’s differential equation for noninteger as well as integer order ... part in 10 12 . MTIEU2 uses continued fraction techniques and is optimized to give accuracy...
  • COULCC

  • Referenced in 12 articles [sw11843]
  • COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments ... found, in general, to the differential equation f ” (x)+g(x)f(x)=0, where...
  • FCC

  • Referenced in 1 article [sw24629]
  • system of linear fractional-order delay-differential equations...
  • AD-TIC

  • Referenced in 1 article [sw17727]
  • order of fractional differentiation are considered for linear fractional anomalous diffusion equations with the Riemann ... required parameters of the fractional diffusion equations by approximately known initial data. These algorithms ... formed by the fractional diffusivity, the order of fractional differentiation and the Laplace variable. Estimations...
  • TFPDE

  • Referenced in 6 articles [sw12622]
  • moment statistics of stochastic partial differential equations with pure jump tempered α-stable (TαS) Lévy ... moment statistics of stochastic reaction-diffusion equations with additive TαS white noises by the probability ... Planck equation that describes the evolution of the density for stochastic overdamped Langevin equations ... different approaches. First, we solve an integral equation for the density by approximating the TαS...