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Stability analysis of a second-order difference scheme for the time-fractional mixed sub-diffusion and diffusion-wave equation
This study investigates a class of initial-boundary value problems pertaining to the time-fractional mixed sub-diffusion and diffusion-wave equation...
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Some Numerical Extrapolation Methods for the Fractional Sub-diffusion Equation and Fractional Wave Equation Based on the L1 Formula
With the help of the asymptotic expansion for the classic L 1 formula and based on the L 1-type compact difference scheme, we propose a temporal...
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Asymptotic analysis of three-parameter Mittag-Leffler function with large parameters, and application to sub-diffusion equation involving Bessel operator
In this paper, we apply the steepest descent method to the Schläfli-type integral representation of the three-parameter Mittag-Leffler function...
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Inverse Problems for Time-Fractional Mixed Equation Involving the Caputo Fractional Derivative
The key object of the present short note is the time-fractional mixed equation consisting of the sub-diffusion and fractional wave equations....
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Analysis of a New NFV Scheme Preserving DMP for Two-Dimensional Sub-diffusion Equation on Distorted Meshes
In this paper, we describe a new nonlinear finite-volume scheme that preserves the discrete maximum principle (DMP) for the two-dimensional...
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Sharp error estimates for spatial-temporal finite difference approximations to fractional sub-diffusion equation without regularity assumption on the exact solution
Finite difference method as a popular numerical method has been widely used to solve fractional diffusion equations. In the general spatial error...
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Solution of the non-linear time-fractional Kudryashov–Sinelshchikov equation using fractional reduced differential transform method
In this research, we analyze the non-linear time-fractional Kudryashov–Sinelshchikov equation, which represents waves induced by pressure inside the...
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Some results on the regional reconstruction of semilinear sub-diffusion fractional processes
The primary objective of the present manuscript is to find and reconstruct the initial state of the considered fractional semilinear system, written...
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Local RBF Method for Transformed Three Dimensional Sub-Diffusion Equations
In this article we study the numerical solution of time fractional 3D sub-diffusion equation in Caputo sense. The time fraction sub-diffusion...
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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 the supercritical fractional diffusion equation with Hardy-type drift
We study the heat kernel of the supercritical fractional diffusion equation with the drift in the critical Hölder space. We show that such a drift...
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Stability, Bifurcation, and Traveling Wave Solutions to the Generalized Time-Fractional Burgers-Huxley Equation
In the field of mathematical sciences and engineering, traveling wave solutions play a crucial role in illustrating numerous nonlinear physical...
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Analyses of the Contour Integral Method for Time Fractional Normal-Subdiffusion Transport Equation
In this work, we theoretically and numerically discuss a class of time fractional normal-subdiffusion transport equation, which depicts a crossover...
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Sub-diffusion for Illiquid Markets
The previous chapters have initiated our journey into the world of processes that are not martingales. We introduce in this chapter a new category of...
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Finite Difference Approximation for the Space-Time Fractional Linear Diffusion Equation Involving the Caputo-Hadamard Fractional Derivative
In this paper, we provide an accurate numerical solution for space-time fractional linear diffusion equation involving the fractinal Caputo-Hadamard...
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Time-fractional nonlinear evolution of dynamic wave propagation using the Burgers’ equation
Fractional derivatives are crucial in diverse contexts, offering a means to extend classical derivatives to noninteger orders. This expansion of...
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Analysis of Time Fractional Diffusion Equation Arising in Ocean Pollution with Different Kernels
The objective of this paper is to look the solution of the ocean oil equations under the three different fractional operators. We analyze the...
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Applications of the Simplest Equation Procedure to Some Fractional Order Differential Equations in Mathematical Physics
The aim of the paper is to find the exact solutions to the nonlinear partial differential equations of fractional-order. The simplest equation...
