Numerical approximation of Riemann‐Liouville definition of fractional derivative: From Riemann‐Liouville to Atangana‐Baleanu
From MaRDI portal
Publication:4623390
DOI10.1002/num.22195zbMath1417.65113OpenAlexW2747592978MaRDI QIDQ4623390
Abdon Atangana, José Francisco Gómez-Aguilar
Publication date: 15 February 2019
Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/num.22195
Related Items (96)
ON EXISTENCE AND STABILITY RESULTS FOR PANTOGRAPH FRACTIONAL BOUNDARY VALUE PROBLEMS ⋮ Numerical study of nonlinear 2D optimal control problems with multi-term variable-order fractional derivatives in the Atangana-Baleanu-Caputo sense ⋮ On a comprehensive model of the novel coronavirus (COVID-19) under Mittag-Leffler derivative ⋮ Modeling the heat flow equation with fractional-fractal differentiation ⋮ A Legendre spectral finite difference method for the solution of non-linear space-time fractional Burger's-Huxley and reaction-diffusion equation with Atangana-Baleanu derivative ⋮ A new approach for solving multi variable orders differential equations with Mittag-Leffler kernel ⋮ Quasi wavelet numerical approach of non-linear reaction diffusion and integro reaction-diffusion equation with Atangana-Baleanu time fractional derivative ⋮ An efficient Mittag-Leffler kernel approach for time-fractional advection-reaction-diffusion equation ⋮ A novel mathematical approach of COVID-19 with non-singular fractional derivative ⋮ On modeling of coronavirus-19 disease under Mittag-Leffler power law ⋮ Novel operational matrices-based finite difference/spectral algorithm for a class of time-fractional Burger equation in multidimensions ⋮ A new approach for solving multi-variable orders differential equations with Prabhakar function ⋮ The plethora of explicit solutions of the fractional KS equation through liquid-gas bubbles mix under the thermodynamic conditions via Atangana-Baleanu derivative operator ⋮ Theoretical and semi-analytical results to a biological model under Atangana-Baleanu-Caputo fractional derivative ⋮ An efficient numerical scheme to solve fractional diffusion-wave and fractional Klein-Gordon equations in fluid mechanics ⋮ ABC fractional order vaccination model for Covid-19 with self-protective measures ⋮ A fully finite difference scheme for time-fractional telegraph equation involving Atangana Baleanu Caputo fractional derivative ⋮ New traveling solutions of the fractional nonlinear KdV and ZKBBM equations with 𝒜ℬℛ fractional operator ⋮ Analytical study of fractional Bratu-type equation arising in electro-spun organic nanofibers elaboration ⋮ A new analysis of fractional Drinfeld-Sokolov-Wilson model with exponential memory ⋮ A fractional order model for hepatitis B virus with treatment via Atangana-Baleanu derivative ⋮ A fractional order HIV/AIDS epidemic model with Mittag-Leffler kernel ⋮ Investigation of complex behaviour of fractal fractional chaotic attractor with Mittag-Leffler Kernel ⋮ A novel approach to find exact solutions of fractional evolution equations with non-singular kernel derivative ⋮ A new modified technique of Adomian decomposition method for fractional diffusion equations with initial-boundary conditions ⋮ Unnamed Item ⋮ Numerical study of Zika model as a mosquito-borne virus with non-singular fractional derivative ⋮ Mathematical modeling of the immune-chemotherapeutic treatment of breast cancer under some control parameters ⋮ Analysis of differential equations involving Caputo-Fabrizio fractional operator and its applications to reaction-diffusion equations ⋮ A comparative study on solving fractional cubic isothermal auto-catalytic chemical system via new efficient technique ⋮ Numerical treatment of delay Salmonella fractional model with Atangana-Baleanu derivative ⋮ INVESTIGATING FRACTAL-FRACTIONAL MATHEMATICAL MODEL OF TUBERCULOSIS (TB) UNDER FRACTAL-FRACTIONAL CAPUTO OPERATOR ⋮ COMPUTATIONAL ANALYSIS OF FRACTIONAL ORDER IMPERFECT TESTING INFECTION DISEASE MODEL ⋮ An efficient numerical scheme for fractional characterization of MHD fluid model ⋮ A novel approach for solving linear and nonlinear time-fractional Schrödinger equations ⋮ Generalized fractional evolution equations driven by fuzzy variational inequalities ⋮ A heat transfer problem with exponential memory and the associated thermal stresses ⋮ Inelastic interaction and blowup new solutions of nonlinear and dispersive long gravity waves ⋮ Numerical solution of <scp>ABC</scp> space–time fractional distributed order reaction–diffusion equation ⋮ A wavelet based numerical scheme for fractional order <scp>SEIR</scp> epidemic of measles by using Genocchi polynomials ⋮ Qualitative study on solutions of piecewise nonlocal implicit fractional differential equations ⋮ Stability analysis of Atangana–Baleanu fractional stochastic differential systems with impulses ⋮ On the algorithmic stability of optimal control with derivative operators ⋮ Agitation of SARS‐CoV‐2 disease (COVID‐19) using ABC fractional‐order modified SEIR model ⋮ On rigorous computational and numerical solutions for the voltages of the electrified transmission range with the day yet distance ⋮ Diverse exact soliton solutions of the time fractional Clannish random Walker's parabolic equation via dual novel techniques ⋮ Fractional Herglotz variational problems with Atangana-Baleanu fractional derivatives ⋮ 2D hereditary thermoelastic application of a thick plate under axisymmetric temperature distribution ⋮ New Direction of Atangana–Baleanu Fractional Derivative with Mittag-Leffler Kernel for Non-Newtonian Channel Flow ⋮ Abundant analytical solutions of the fractional nonlinear (2 + 1)-dimensional BLMP equation arising in incompressible fluid ⋮ Numerical solutions of integrodifferential equations of Fredholm operator type in the sense of the Atangana-Baleanu fractional operator ⋮ Numerical approximations of Atangana-Baleanu Caputo derivative and its application ⋮ Green function's properties and existence theorems for nonlinear singular-delay-fractional differential equations ⋮ Numerical analysis for the Klein-Gordon equation with mass parameter ⋮ Approximation methods for solving fractional equations ⋮ New results on existence in the framework of Atangana-Baleanu derivative for fractional integro-differential equations ⋮ New predictor‐corrector scheme for solving nonlinear differential equations with Caputo‐Fabrizio operator ⋮ Solutions of the linear and nonlinear differential equations within the generalized fractional derivatives ⋮ On the recurrent computation of fractional operator with Mittag-Leffler kernel ⋮ New numerical analysis of Riemann-Liouville time-fractional Schrödinger with power, exponential decay, and Mittag-Leffler laws ⋮ Local fractional homotopy analysis method for solving non-differentiable problems on Cantor sets ⋮ New exact solitary waves solutions to the fractional Fokas-Lenells equation via Atangana-Baleanu derivative operator ⋮ Unnamed Item ⋮ The generalized bifurcation method for deriving exact solutions of nonlinear space-time fractional partial differential equations ⋮ A class of shifted high-order numerical methods for the fractional mobile/immobile transport equations ⋮ A high-order scheme for fractional ordinary differential equations with the Caputo-Fabrizio derivative ⋮ Numerical solution of time-fractional three-species food chain model arising in the realm of mathematical ecology ⋮ A wavelet method for nonlinear variable-order time fractional 2D Schrödinger equation ⋮ Existence of mild solutions for impulsive neutral Hilfer fractional evolution equations ⋮ A numerical investigation of Caputo time fractional Allen-Cahn equation using redefined cubic B-spline functions ⋮ Approximate analytical solution of fractional order biochemical reaction model and its stability analysis ⋮ Study of fuzzy fractional nonlinear equal width equation in the sense of novel operator ⋮ Numerical patterns in system of integer and non-integer order derivatives ⋮ S-asymptotically \(\omega\)-periodic mild solutions and stability analysis of Hilfer fractional evolution equations ⋮ Novel analysis of fuzzy physical models by generalized fractional fuzzy operators ⋮ Recovering the space source term for the fractional-diffusion equation with Caputo-Fabrizio derivative ⋮ SOLUTION OF NON-LINEAR FRACTIONAL DIFFERENTIAL EQUATIONS BY VARIATIONAL ITERATION METHOD AND APPLICATIONS ⋮ Local fractional Laplace homotopy analysis method for solving non-differentiable wave equations on Cantor sets ⋮ Generalized squared remainder minimization method for solving multi-term fractional differential equations ⋮ Local fractional Newton's inequalities involving generalized harmonic convex functions ⋮ On abundant new solutions of two fractional complex models ⋮ Riemann-Liouville derivative over the space of integrable distributions ⋮ Traveling wave solutions in closed form for some nonlinear fractional evolution equations related to conformable fractional derivative ⋮ A numerical approach for fractional partial differential equations by using Ritz approximation ⋮ Further fresh and general traveling wave solutions to some fractional order nonlinear evolution equations in mathematical physics ⋮ Numerical solution of fractional boundary value problem with Caputo-Fabrizio and its fractional integral ⋮ DYNAMICS OF SIR MATHEMATICAL MODEL FOR COVID-19 OUTBREAK IN PAKISTAN UNDER FRACTAL-FRACTIONAL DERIVATIVE ⋮ MODELING AND ANALYSIS OF NOVEL COVID-19 UNDER FRACTAL-FRACTIONAL DERIVATIVE WITH CASE STUDY OF MALAYSIA ⋮ Existence and numerical analysis of imperfect testing infectious disease model in the sense of fractional-order operator ⋮ Mean-square exponential stability of impulsive conformable fractional stochastic differential system with application on epidemic model ⋮ MATHEMATICAL AND STATISTICAL ANALYSIS OF RL AND RC FRACTIONAL-ORDER CIRCUITS ⋮ ON THE NEW EXPLICIT SOLUTIONS OF THE FRACTIONAL NONLINEAR SPACE-TIME NUCLEAR MODEL ⋮ APPLICATIONS OF BI-FRAMELET SYSTEMS FOR SOLVING FRACTIONAL ORDER DIFFERENTIAL EQUATIONS ⋮ Nonlinear regularized long-wave models with a new integral transformation applied to the fractional derivative with power and Mittag-Leffler kernel ⋮ Analysis of time-fractional \(\phi^4\)-equation with singular and non-singular kernels ⋮ On stability analysis and existence of positive solutions for a general non-linear fractional differential equations
This page was built for publication: Numerical approximation of Riemann‐Liouville definition of fractional derivative: From Riemann‐Liouville to Atangana‐Baleanu
