scientific article

From MaRDI portal
Publication:2741107

zbMath1138.91444MaRDI QIDQ2741107

Rudolf Gorenflo, Marco Raberto, Enrico Scalas, Francesco Mainardi

Publication date: 9 September 2001


Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.



Related Items

A new approach to space fractional differential equations based on fractional order Euler polynomialsThree Landweber iterative methods for solving the initial value problem of time-fractional diffusion-wave equation on spherically symmetric domainLimit theorems for some continuous-time random walksStrong approximation of stochastic differential equations driven by a time-changed Brownian motion with time-space-dependent coefficientsTwo finite difference schemes for time fractional diffusion-wave equationParameter estimation of fractional uncertain differential equations via Adams methodSolving the fractional nonlinear Bloch system using the multi-step generalized differential transform methodQuadratic Spline Function for the Approximate Solution of an Intermediate Space-Fractional Advection Diffusion EquationOn the convergence of quadratic variation for compound fractional Poisson processesFirst-exit times of an inverse Gaussian processHigh-order compact finite volume scheme for the 2D multi-term time fractional sub-diffusion equationFractional Euler Limits and their ApplicationsNumerical study on fractional-order Lotka-Volterra model with spectral method and Adams-Bashforth-Moulton methodAnalysis of a system of autonomous fractional differential equationsComputing Fractional Laplacians on Complex-Geometry Domains: Algorithms and SimulationsNovel operational matrix method for the numerical solution of nonlinear reaction-advection-diffusion equation of fractional orderA fractional phase-field model for two-phase flows with tunable sharpness: algorithms and simulationsNon-Markovian process with variable memory functionsDistributed order model of labor migrationError estimates of spectral Galerkin methods for a linear fractional reaction-diffusion equationA generalized scheme based on shifted Jacobi polynomials for numerical simulation of coupled systems of multi-term fractional-order partial differential equationsChebyshev Spectral Approximation for Diffusion Equations with Distributed Order in TimeLearning parameters of a system of variable order fractional differential equationsOn the fractional Poisson process and the discretized stable subordinatorStatistical and transport properties of a one-dimensional random walk with periodically distributed trapping intervalsDetermination of an unknown source term for an inverse source problem of the time-fractional equationPoincaré-type inequalities for stable densitiesConvergence analysis of a LDG method for tempered fractional convection–diffusion equationsSDEs driven by a time-changed Lévy process and their associated time-fractional order pseudo-differential equationsAn analytical approach for the fractional-order Hepatitis B model using new operatorFractional Deterministic Factor Analysis of Economic Processes with Memory and NonlocalityAnomalous waiting times in high-frequency financial dataLie symmetry analysis to general time-fractional Korteweg-de Vries equationsElasticity for economic processes with memory: fractional differential calculus approachFractional kinetic equations driven by Gaussian or infinitely divisible noiseAnomalous Diffusions in Option Prices: Connecting Trade Duration and the Volatility Term StructureGeneralized Master Equations for Random Walks with Time-Dependent Jump SizesStrong analytic solutions of fractional Cauchy problemsMeshless analysis of two-dimensional two-sided space-fractional wave equation based on improved moving least-squares approximationNumerical Solution of the Coupled System of Nonlinear Fractional Ordinary Differential EquationsApplication of modified decomposition method for the analytical solution of space fractional diffusion equationSpace-time fractional derivative operatorsNovel operational matrices-based method for solving fractional-order delay differential equations via shifted Gegenbauer polynomialsPointwise stability of shock wave for 2D anisotropic viscous conservation laws with large perturbationCOMPARISON PRINCIPLES FOR HADAMARD-TYPE FRACTIONAL DIFFERENTIAL EQUATIONSMesoscopic Modeling of Stochastic Reaction-Diffusion Kinetics in the Subdiffusive RegimeStepwise regularization method for a nonlinear Riesz-Feller space-fractional backward diffusion problemNumerical investigation of the nonlinear modified anomalous diffusion processA numerical scheme based on Bernoulli wavelets and collocation method for solving fractional partial differential equations with Dirichlet boundary conditionsDiscrete and continuous random walk models for space-time fractional diffusionFokker-Planck-Kolmogorov equations associated with time-changed fractional Brownian motionDiscrete and continuous random walk models for space-time fractional diffusionBrownian subordinators and fractional Cauchy problemsError Analysis of a High Order Method for Time-Fractional Diffusion EquationsTwo-dimensional Müntz-Legendre hybrid functions: theory and applications for solving fractional-order partial differential equationsAn iterative method for backward time‐fractional diffusion problemSeries representation of the pricing formula for the European option driven by space-time fractional diffusionPhillips model with exponentially distributed lag and power-law memoryNumerical solution of a modified anomalous diffusion equation with nonlinear source term through meshless singular boundary methodFractional calculus in economic growth modelling of the group of sevenOn Riesz derivativeFractional cable problem in the frame of meshless singular boundary methodProfessor Rudolf Gorenflo and his contribution to fractional calculusFractional Fokker-Planck-Kolmogorov type equations and their associated stochastic differential equationsAnd I say to myself: “What a fractional world!”Fractional-order Legendre-Laguerre functions and their applications in fractional partial differential equationsFinite difference methods for two-dimensional fractional dispersion equationA numerical approach for fractional partial differential equations by using Ritz approximationFinite difference approximations for two-sided space-fractional partial differential equationsHigh-order fractional partial differential equation transform for molecular surface constructionNumerical Solutions of Time Fractional Korteweg--de Vries Equation and Its Stability AnalysisNumerical solutions for fractional optimal control problems by using generalised fractional-order Chebyshev waveletsLevi-Civita cylinders with fractional angular deficitINVESTIGATION OF FRACTIONAL ORDER SINE-GORDON EQUATION USING LAPLACE ADOMIAN DECOMPOSITION METHODEffective numerical treatment of sub-diffusion equation with non-smooth solutionFractional-order Bessel wavelet functions for solving variable order fractional optimal control problems with estimation errorA compact ADI Crank–Nicolson difference scheme for the two-dimensional time fractional subdiffusion equationSolving the backward problem in Riesz-Feller fractional diffusion by a new nonlocal regularization methodSmall ball probabilities for a class of time-changed self-similar processesA stochastic solution with Gaussian stationary increments of the symmetric space-time fractional diffusion equationFinite difference approximations for fractional advection-dispersion flow equationsNumerical solution of fractional diffusion-wave equation based on fractional multistep methodA finite difference scheme based on cubic trigonometric B-splines for a time fractional diffusion-wave equationStability and convergence of a new finite volume method for a two-sided space-fractional diffusion equationStability and convergence analysis of a class of continuous piecewise polynomial approximations for time-fractional differential equationsA fractional calculus interpretation of the fractional volatility modelFractional econophysics: market price dynamics with memory effectsExponential-sum-approximation technique for variable-order time-fractional diffusion equationsTime fractional capital-induced labor migration modelConvergence analysis of a LDG method for time-space tempered fractional diffusion equations with weakly singular solutionsAn efficient analysis for \(N\)-soliton, lump and lump-kink solutions of time-fractional \((2+1)\)-Kadomtsev-Petviashvili equationTempered fractional calculusTheoretical and computational analysis of nonlinear fractional integro-differential equations via collocation methodA second-order accurate numerical method for the two-dimensional fractional diffusion equationExistence, uniqueness, and approximate solutions for the general nonlinear distributed-order fractional differential equations in a Banach spaceRobin initial-boundary value problem for nonlinear Schrödinger equation with potentialFractional equations via convergence of formsOn the fractional diffusion-advection-reaction equation in \(\mathbb{R}\)Logistic map with memory from economic modelTime-dependent fractional dynamics with memory in quantum and economic physicsFirst exit times of non-linear dynamical systems in \(\mathbb R^{d}\) perturbed by multifractal Lévy noiseGeneralized fractional master equation for self-similar stochastic processes modelling anomalous diffusionA fractional spectral method with applications to some singular problemsApproximate solution of the fractional advection-dispersion equationFinite element method for nonlinear Riesz space fractional diffusion equations on irregular domainsOn Tikhonov's method and optimal error bound for inverse source problem for a time-fractional diffusion equationContinuous time random walk based theory for a one-dimensional coarsening modelInvariant analysis with conservation laws for the time fractional Drinfeld-Sokolov-Satsuma-Hirota equationsCagan model of inflation with power-law memory effectsBoundary conditions for fractional diffusionInvariant analysis and conservation laws for the time fractional \((2+1)\)-dimensional Zakharov-Kuznetsov modified equal width equation using Lie group analysisAn efficient iterative approach for three-dimensional modified anomalous fractional sub-diffusion equations on a large domainA fractional Landweber method for solving backward time-fractional diffusion problemConcept of dynamic memory in economicsDirect transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problemsFractional-order susceptible-infected model: definition and applications to the study of COVID-19 main proteaseLandweber iterative regularization method for identifying the unknown source of the time-fractional diffusion equationOptimal error estimate of the Legendre spectral approximation for space-fractional reaction-advection-diffusion equationA fractional order SIR epidemic model with nonlinear incidence rateAn efficient meshless method based on RBFs for the time fractional diffusion-wave equationFormulation and solution to time-fractional generalized Korteweg-de Vries equation via variational methodsA generalized fractional-order Chebyshev wavelet method for two-dimensional distributed-order fractional differential equationsNumerical solutions of nonlinear fractional partial differential equations arising in spatial diffusion of biological populationsPower law and entropy analysis of catastrophic phenomenaA second order finite difference-spectral method for space fractional diffusion equationsOptimal error bound and simplified Tikhonov regularization method for a backward problem for the time-fractional diffusion equationPartial chaos suppression in a fractional order macroeconomic modelApproximation solution of fractional partial differential equations by neural networksContinuity of solutions of a class of fractional equationsA numerical approach for multi-variable orders differential equations using Jacobi polynomialsMixtures of compound Poisson processes as models of tick-by-tick financial dataA compact locally one-dimensional method for fractional diffusion-wave equationsContinuous-time random walk and parametric subordination in fractional diffusionClassical and nonclassical Lie symmetry analysis to a class of nonlinear time-fractional differential equationsFractional-in-time and multifractional-in-space stochastic partial differential equationsLaguerre functions and their applications to tempered fractional differential equations on infinite intervalsTriangular array limits for continuous time random walksFrom tick data to semimartingalesFractional Landweber iterative regularization method for identifying the unknown source of the time-fractional diffusion problemThe implicit midpoint method for the modified anomalous sub-diffusion equation with a nonlinear source termNumerical solution for diffusion equations with distributed order in time using a Chebyshev collocation methodA second-order operator splitting Fourier spectral method for fractional-in-space reaction-diffusion equationsRegularization of inverse source problem for fractional diffusion equation with Riemann-Liouville derivativeReprint of: boundary conditions for fractional diffusionA preconditioned fast finite difference method for space-time fractional partial differential equationsComputational solutions of the tempered fractional wave-diffusion equationA foundational approach to the Lie theory for fractional order partial differential equationsA meshless point collocation method for 2-D multi-term time fractional diffusion-wave equationApproximation of solutions of fractional-order delayed cellular neural network on \([0,\infty)\)Solving the backward problem for space-fractional diffusion equation by a fractional Tikhonov regularization methodLie symmetry analysis, conservation laws and similarity reductions of Newell-Whitehead-Segel equation of fractional orderFractional Hermite interpolation using RBFs in high dimensions over irregular domains with applicationOn the numerical solution of space-time fractional diffusion modelsAn analytic algorithm for the space-time fractional advection-dispersion equationNumerical methods for fractional partial differential equations with Riesz space fractional derivativesModeling extreme-event precursors with the fractional diffusion equationA box-type scheme for fractional sub-diffusion equation with Neumann boundary conditionsA numerical approach for fractional order Riccati differential equation using B-spline operational matrixAnalytical solution for the space fractional diffusion equation by two-step Adomian decomposition methodFront dynamics in fractional-order epidemic modelsReconstruction of the time-dependent source term in a stochastic fractional diffusion equationCopula based multivariate semi-Markov models with applications in high-frequency financeThe linear B-spline scaling function operational matrix of fractional integration and its applications in solving fractional-order differential equationsA spectral Galerkin method for the fractional order diffusion and wave equationCubic polynomial spline scheme for fractional boundary value problems with left and right fractional operatorsPreconditioned iterative methods for space-time fractional advection-diffusion equationsA method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equationsNumerical method based on Galerkin approximation for the fractional advection-dispersion equationA new stable algorithm for fractional Navier-Stokes equation in polar coordinateNumerical solutions of coupled systems of fractional order partial differential equationsA random walk approach to transport in tissues and complex media: from microscale descriptions to macroscale modelsA fractional Hawkes processSome recent advances in theory and simulation of fractional diffusion processesWaiting-times and returns in high-frequency financial data: An empirical studyDifference numerical solutions for time-space fractional advection diffusion equationEfficient numerical techniques for computing the Riesz fractional-order reaction-diffusion models arising in biologySolving the Riesz-Feller space-fractional backward diffusion problem by a generalized Tikhonov method