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   Articles with "distributed order" as a keyword



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A numerical scheme to solve a class of two-dimensional nonlinear time-fractional diffusion equations of distributed order

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recommendations! Published in 2020 at "Engineering With Computers"

DOI: 10.1007/s00366-020-01185-7

Abstract: This article is devoted to obtain the numerical solution for a class of nonlinear two-dimensional distributed-order time-fractional diffusion equations. We discretize the problem by using a finite difference scheme in the time direction. Then, we solve… read more here.

Keywords: fractional diffusion; distributed order; time fractional; time ... See more keywords
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High-Order Numerical Method for Solving a Space Distributed-Order Time-Fractional Diffusion Equation

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recommendations! Published in 2021 at "Acta Mathematica Scientia"

DOI: 10.1007/s10473-021-0311-1

Abstract: This article proposes a high-order numerical method for a space distributed-order time-fractional diffusion equation. First, we use the mid-point quadrature rule to transform the space distributed-order term into multi-term fractional derivatives. Second, based on the… read more here.

Keywords: time; space distributed; order; method ... See more keywords
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$$\beta $$ β -Robust Superconvergent Analysis of a Finite Element Method for the Distributed Order Time-Fractional Diffusion Equation

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recommendations! Published in 2022 at "Journal of Scientific Computing"

DOI: 10.1007/s10915-021-01726-2

Abstract: A distributed order time fractional diffusion equation whose solution has a weak singularity near the initial time $$t = 0$$ t = 0 is considered. The numerical method of the paper uses the well-known L1… read more here.

Keywords: beta robust; time; order time; distributed order ... See more keywords
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A Legendre collocation method for distributed-order fractional optimal control problems

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recommendations! Published in 2018 at "Nonlinear Dynamics"

DOI: 10.1007/s11071-017-4038-4

Abstract: In many dynamic processes, the fractional differential operators not only appear as discrete fractional, but they also possess a continuous nature in a sense that their order is distributed over a given range. This paper… read more here.

Keywords: distributed order; order; method; order fractional ... See more keywords
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Application of variable- and distributed-order fractional operators to the dynamic analysis of nonlinear oscillators

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recommendations! Published in 2020 at "Nonlinear Dynamics"

DOI: 10.1007/s11071-020-05488-8

Abstract: Many physical processes in nature exhibit complex dynamics that result from a combination of multiscale, nonlinear, non-local, and memory effects. Recent experimental measurements conducted in a variety of physical domains have shown that, at the… read more here.

Keywords: distributed order; order; fractional operators; application variable ... See more keywords
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Shifted fractional Jacobi spectral algorithm for solving distributed order time-fractional reaction–diffusion equations

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recommendations! Published in 2019 at "Computational and Applied Mathematics"

DOI: 10.1007/s40314-019-0845-1

Abstract: This paper proposes a new method for solving distributed order time-fractional reaction–diffusion equations (DO-TFRDEs). Extended versions of the shifted Jacobi–Gauss–Lobatto and shifted fractional order Jacobi–Gauss–Radau collocation methods are developed for reducing the DO-TFRDEs to systems… read more here.

Keywords: order; time fractional; distributed order; fractional reaction ... See more keywords
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Fractional Backward Differential Formulas for the Distributed-Order Differential Equation with Time Delay

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recommendations! Published in 2018 at "Bulletin of the Iranian Mathematical Society"

DOI: 10.1007/s41980-018-0191-x

Abstract: In this paper, we investigate the fractional backward differential formulas for the distributed-order differential equation with time delay. The mid-point quadrature rule is used to approximate the distributed-order equation by a multi-term fractional form. Next… read more here.

Keywords: distributed order; backward differential; differential formulas; fractional backward ... See more keywords
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Numerical approach for a class of distributed order time fractional partial differential equations

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recommendations! Published in 2019 at "Applied Numerical Mathematics"

DOI: 10.1016/j.apnum.2018.09.019

Abstract: Abstract The numerical solution of distributed order time fractional partial differential equations based on the midpoint quadrature rule and linear B-spline interpolation is studied. The proposed discretization algorithm follows the Du Fort–Frankel method. The unconditional… read more here.

Keywords: fractional partial; partial differential; differential equations; time fractional ... See more keywords
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A variably distributed-order time-fractional diffusion equation: Analysis and approximation

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recommendations! Published in 2020 at "Computer Methods in Applied Mechanics and Engineering"

DOI: 10.1016/j.cma.2020.113118

Abstract: Abstract We prove the wellposedness and smoothing properties of the initial–boundary value problem of a variably distributed-order time-fractional diffusion partial differential equation in multiple space dimensions, which models the subdiffusive transport of solutes traveling through… read more here.

Keywords: fractional diffusion; distributed order; order; time fractional ... See more keywords
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An RBF based meshless method for the distributed order time fractional advection–diffusion equation

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recommendations! Published in 2018 at "Engineering Analysis with Boundary Elements"

DOI: 10.1016/j.enganabound.2018.08.007

Abstract: Abstract Distributed order operators and differential equations have been applied to model physical phenomena. Then the numerical methods for these problems are required. In this paper, we consider a meshless method for solving a distributed… read more here.

Keywords: distributed order; order; time fractional; order time ... See more keywords
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Decay of solutions to parabolic-type problem with distributed order Caputo derivative

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recommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"

DOI: 10.1016/j.jmaa.2018.04.067

Abstract: Abstract We consider the decay of solution to a fractional diffusion equation with distributed order Caputo derivative. We assume that the elliptic operator is time-dependent and that the weight function, contained in the definition of… read more here.

Keywords: order caputo; decay solutions; caputo derivative; distributed order ... See more keywords