Lattice fractional diffusion equation of random order
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DOI: 10.1002/mma.3644
Abstract: The discrete fractional calculus is used to fractionalize difference equations. Simulations of the fractional logistic map unravel that the chaotic solution is conveniently obtained. Then a Riesz fractional difference is defined for fractional partial difference… read more here.
Keywords: fractional diffusion; equation random; lattice fractional; random order ... See more keywords
Existence and regularity results of a backward problem for fractional diffusion equations
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DOI: 10.1002/mma.5781
Abstract: In this paper, we study a backward problem for an inhomogeneous fractional diffusion equation in a bounded domain. By applying the properties of Mittag‐Leffler functions and the method of eigenvalue expansion, we establish some results… read more here.
Keywords: fractional diffusion; problem; existence regularity; backward problem ... See more keywords
A numerical method for space‐fractional diffusion models with mass‐conserving boundary conditions
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DOI: 10.1002/mma.9310
Abstract: The study of the spread of epidemics has gained significant attention in recent years, due to ongoing and recurring outbreaks of diseases such as COVID‐19, dengue, Ebola, and West Nile virus. In particular, modeling the… read more here.
Keywords: fractional diffusion; reflecting boundary; conserving boundary; boundary conditions ... See more keywords
Inverse source problem with a posteriori boundary measurement for fractional diffusion equations
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DOI: 10.1002/mma.9432
Abstract: In this article we study inverse source problems for time-fractional diffusion equations from \textit{a posteriori} boundary measurement. Using the memory effect of these class of equations, we solve these inverse problems for several class of… read more here.
Keywords: fractional diffusion; time; diffusion equations; inverse source ... See more keywords
Motility Switching and Front–Back Synchronisation in Polarised Cells
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DOI: 10.1007/s00332-022-09791-z
Abstract: The combination of protrusions and retractions in the movement of polarised cells leads to understand the effect of possible synchronisation between the two ends of the cells. This synchronisation, in turn, could lead to different… read more here.
Keywords: fractional diffusion; synchronisation; polarised cells; switching front ... See more keywords
Semi-analytical solution for time-fractional diffusion equation based on finite difference method of lines (MOL)
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DOI: 10.1007/s00366-018-0595-5
Abstract: In this article, we apply the method of lines (MOL) for solving the time-fractional diffusion equations (TFDEs). The use of MOL yields a system of fractional differential equations with the initial value. The solution of… read more here.
Keywords: time fractional; method lines; lines mol; fractional diffusion ... See more keywords
A numerical scheme to solve a class of two-dimensional nonlinear time-fractional diffusion equations of distributed order
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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
Efficient preconditioner of one-sided space fractional diffusion equation
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DOI: 10.1007/s10543-018-0699-8
Abstract: In this paper, we propose an efficient preconditioner for the linear systems arising from the one-sided space fractional diffusion equation with variable coefficients. The shifted Gr$$\ddot{\mathrm{u}}$$u¨nwald formula is employed to discretize the one-sided Riemann–Liouville fractional… read more here.
Keywords: efficient preconditioner; fractional diffusion; one sided; sided space ... See more keywords
Optimized Overlapping Schwarz Waveform Relaxation for a Class of Time-Fractional Diffusion Problems
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DOI: 10.1007/s10915-017-0379-x
Abstract: For parabolic PDEs with integer-order temporal derivative, if we use the Schwarz waveform relaxation (SWR) algorithm with Robin transmission conditions as the solver, the so-called equioscillation principle is an important concept to get a good… read more here.
Keywords: fractional diffusion; time fractional; time; waveform relaxation ... See more keywords
Optimization with Respect to Order in a Fractional Diffusion Model: Analysis, Approximation and Algorithmic Aspects
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DOI: 10.1007/s10915-018-0703-0
Abstract: We consider an identification (inverse) problem, where the state $${\mathsf {u}}$$u is governed by a fractional elliptic equation and the unknown variable corresponds to the order $$s \in (0,1)$$s∈(0,1) of the underlying operator. We study… read more here.
Keywords: fractional diffusion; optimization respect; respect order; order ... See more keywords
Mixed FEM for Time-Fractional Diffusion Problems with Time-Dependent Coefficients
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DOI: 10.1007/s10915-020-01236-7
Abstract: In this paper, a mixed finite element method is applied in spatial directions while keeping time variable continuous to a class of time-fractional diffusion problems with time-dependent coefficients on a bounded convex polygonal domain. Based… read more here.
Keywords: problems time; fractional diffusion; time fractional; time ... See more keywords