A new numerical method for solving fractional delay differential equations

DOI10.1007/s40314-019-0951-0zbMath1449.65142OpenAlexW2978022241MaRDI QIDQ2326359

Varsha Daftardar-Gejji, Aman Jhinga

Publication date: 7 October 2019

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40314-019-0951-0

zbMATH Keywords

delaynumerical methodsfractional differential equationsCaputo fractional derivative

Mathematics Subject Classification ID

Error bounds for numerical methods for ordinary differential equations (65L70) Functional-differential equations with fractional derivatives (34K37) Numerical methods for functional-differential equations (65L03)

Related Items (17)

On a new system of fractional delay differential equations coupled with fuzzy variational inequalities ⋮ Solving fractional time-delay diffusion equation with variable-order derivative based on shifted Legendre-Laguerre operational matrices ⋮ Analysis of a finite difference method based on L1 discretization for solving multi‐term fractional differential equation involving weak singularity ⋮ Analytical solutions of linear delay-differential equations with Dirac delta function inputs using the Laplace transform ⋮ A novel shifted Jacobi operational matrix method for nonlinear multi‐terms delay differential equations of fractional variable‐order with periodic and anti‐periodic conditions ⋮ A NEW FORM OF L1-PREDICTOR–CORRECTOR SCHEME TO SOLVE MULTIPLE DELAY-TYPE FRACTIONAL ORDER SYSTEMS WITH THE EXAMPLE OF A NEURAL NETWORK MODEL ⋮ Simultaneous identification of time-delay parameter and fractional order in nonlinear fractional delay differential equation ⋮ A streamlined numerical method to treat fractional nonlinear terminal value problems with multiple delays appearing in biomathematics ⋮ On initial conditions for fractional delay differential equations ⋮ A novel finite difference technique with error estimate for time fractional partial integro-differential equation of Volterra type ⋮ A robust computational framework for analyzing fractional dynamical systems ⋮ A Qualitative Theory of Time Delay Nonlinear Fractional-Order Systems ⋮ Higher order numerical schemes for the solution of fractional delay differential equations ⋮ On exact and discretized stability of a linear fractional delay differential equation ⋮ On stability analysis of hybrid fractional boundary value problem ⋮ An efficient method for linear fractional delay integro-differential equations ⋮ An efficient numerical scheme for solving a fractional-order system of delay differential equations

Uses Software

• DELSOL

Cites Work

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• A new predictor-corrector method for fractional differential equations
• Fractional Bloch equation with delay
• Analysis of nonlinear dynamics and chaos in a fractional order financial system with time delay
• Delay differential equations: with applications in population dynamics
• Antisynchronization of nonidentical fractional-order chaotic systems using active control
• Convergence of the new iterative method
• An iterative method for solving nonlinear functional equations
• Fractional high order methods for the nonlinear fractional ordinary differential equation
• On the existence and the uniqueness theorem for fractional differential equations with bounded delay within Caputo derivatives
• DELSOL -- a numerical code for the solution of systems of delay- differential equations
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• The accuracy and stability of an implicit solution method for the fractional diffusion equation
• Detailed error analysis for a fractional Adams method
• A predictor-corrector approach for the numerical solution of fractional differential equations
• Modifications of the optimal velocity traffic model to include delay due to driver reaction time
• Solving fractional delay differential equations: a new approach
• A new finite-difference predictor-corrector method for fractional differential equations
• Finite difference/spectral approximations for the time-fractional diffusion equation
• Analysis and numerical methods for fractional differential equations with delay
• A fully discrete difference scheme for a diffusion-wave system
• Nonlinear multi-order fractional differential equations with periodic/anti-periodic boundary conditions
• Existence and uniqueness theorem for a class of delay differential equations with left and right Caputo fractional derivatives

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