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High-order spectral collocation method using tempered fractional Sturm–Liouville eigenproblems
This paper presents an accurate exponential tempered fractional spectral collocation method (TFSCM) to solve one-dimensional and time-dependent...
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ADI Finite Element Galerkin Methods for Two-dimensional Tempered Fractional Integro-differential Equations
Three alternating direction implicit (ADI) finite element Galerkin methods for solving two-dimensional tempered fractional integro-differential...
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Direct Method of Moving Planes for Tempered Fractional Laplacian Equations
In this paper, we extend the direct method of moving planes to tempered fractional Laplacian equations. To carry out the method, a narrow region...
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Mean Value and Taylor-Type Results for Tempered Fractional Derivatives
In this paper, we deal with the mean value theorem for tempered fractional operators, some properties with monotone functions and the Taylor theorem...
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A novel banded preconditioner for coupled tempered fractional diffusion equation generated from the regime-switching CGMY model
With the growing popularity of the regime-switching Lévy processes model in option pricing, the coupled tempered fractional diffusion equation...
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New theories and applications of tempered fractional differential equations
In this paper, we develop theories, properties and applications of a new technique in tempered fractional calculus called the Tempered Fractional...
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Analytical and numerical investigation on the tempered time-fractional operator with application to the Bloch equation and the two-layered problem
In the continuous-time random walk model, the time-fractional operator usually expresses an infinite waiting time probability density. Different from...
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Pricing Vulnerable Options in Fractional Brownian Markets: a Partial Differential Equations Approach
As defaultable options are subject to default risks in over-the-counter (OTC) markets, vulnerable options are one of the financial securities closely...
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Solvability of an infinite system of fractional differential equations with p-Laplacian operator in a new tempered sequence space
In this article, an infinite system of three point boundary value problem of p -Laplacian operator is considered for the existence of solution in a...
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A second-order finite difference scheme for nonlinear tempered fractional integrodifferential equations in three dimensions
In this paper, we provide a numerical solution for the nonlinear tempered fractional integrodifferential equation in three dimensions. We use the...
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Crank-Nicolson ADI finite difference/compact difference schemes for the 3D tempered integrodifferential equation associated with Brownian motion
This paper proposes and analyzes a tempered fractional integrodifferential equation in three-dimensional (3D) space. The Crank-Nicolson (CN) method...
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Convergence Analysis of a LDG Method for Time–Space Tempered Fractional Diffusion Equations with Weakly Singular Solutions
A class of time–space tempered fractional diffusion equations is considered in this paper. The solution of these problems generally have a weak...
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A tempered subdiffusive Black–Scholes model
In this paper, we focus on the tempered subdiffusive Black–Scholes model. The main part of our work consists of the finite difference method as a...
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Numerical methods for forward fractional Feynman–Kac equation
Fractional Feynman–Kac equation governs the functional distribution of the trajectories of anomalous diffusion. The non-commutativity of the integral...
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On some direct and inverse problems for an integro-differential equation
The direct and two inverse problems defined for an integro-differential equation on a bounded domain have been considered. The spectral problem of...
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Integral transforms suitable for solving fractional differential equations
The purpose of this article is to obtain appropriate tools for solving fractional differential equations that are flexible enough to adapt to...
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Hitting properties of generalized fractional kinetic equation with time-fractional noise
This paper investigates the hitting properties of a system of generalized fractional kinetic equations driven by Gaussian noise that is fractional in...