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

MittagLeffler
 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., noninteger) 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 integrodifferential 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 fractionalorder 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]
 Predictorcorrector PECE method for fractional differential equations. MATLAB Central File Exchange. FDE12 solves ... problem for a nonlinear differential equation of fractional order (FDE). This is an implementation...

YUIMA
 Referenced in 45 articles
[sw11399]
 discretely observed fractional OrnsteinUhlenbeck 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 firstorder...

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 PhysicsInformed Neural Networks. Physicsinformed neural networks (PINNs ... effective in solving integerorder partial differential equations (PDEs) based on scattered and noisy data ... explicitly encoded into the NN using automatic differentiation, while the sum of the meansquared ... PINNs to fractional PINNs (fPINNs) to solve spacetime fractional advectiondiffusion equations (fractional ADEs...

Kernel compression
 Referenced in 1 article
[sw22517]
 Kernel compression time stepping schemes for fractional differential equations. Highorder accurate, adaptive, kernel compression ... schemes for fractional differential equations. An implementation of efficient and accurate kernel compression timestepping ... 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 continuedfraction 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 fractionalorder delaydifferential equations...

ADTIC
 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 αstable (TαS) Lévy ... moment statistics of stochastic reactiondiffusion 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...