Results 41 to 50 of about 2,952,428 (298)
Solutions of the Fractional Reaction Equation and the Fractional Diffusion Equation [PDF]
, 2009 In view of the role of reaction equations in physical problems, the authors derive the explicit solution of a fractional reaction equation of general character, that unifies and extends earlier results. Further, an alternative shorter method based on a result developed by the authors is given to derive the solution of a fractional diffusion equation ...
Saxena, R. K. +2 more
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A new class of travelling wave solutions for local fractional diffusion differential equations
Advances in Difference Equations, 2020 In this paper, we investigate a 3-D diffusion equation within the scope of the local fractional derivative. For this model, we establish local fractional vector operators and a local fractional Laplace operator defined on Cantor-type cylindrical ...
Ziyue Shi, Wei Qi, Jing Fan
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Mathematical Modelling and Analysis, 2021 An inverse problem of determining a time dependent source term along with diffusion/temperature concentration from a non-local over-specified condition for a space-time fractional diffusion equation is considered.
Salman A. Malik +2 more
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Fractional Diffusion Models for the Atmosphere of Mars
Fractal and Fractional, 2017 The dust aerosols floating in the atmosphere of Mars cause an attenuation of the solar radiation traversing the atmosphere that cannot be modeled through the use of classical diffusion processes.
Salvador Jiménez +3 more
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Annales Mathematicae Silesianae, 2023 In this paper, we use the finite element method to solve the fractional space-time diffusion equation over finite fields. This equation is obtained from the standard diffusion equation by replacing the first temporal derivative with the new fractional ...
Boutiba Malika +2 more
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Applied Sciences, 2021 A generalized mathematical model of the radial groundwater flow to or from a well is studied using the time-fractional derivative with Mittag-Lefler kernel.
Nehad Ali Shah +4 more
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Cauchy problem for nonlocal diffusion equations modelling Lévy flights
Electronic Journal of Qualitative Theory of Differential Equations, 2022 In the present paper, we study the time-space fractional diffusion equation involving the Caputo differential operator and the fractional Laplacian. This equation describes the Lévy flight with the Brownian motion component and the drift component. First,
Chung-Sik Sin
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Numerical Study Of The Spatial Fractional Advection-Diffusion Equation
, 2021 Here we discuss the advection-diffusion equation with diffusion fractional in one dimension. The study provides a Riemann-Liouville fractional derivative (RLFD) to obtain an implicit scheme of space fractional advection-diffusion equation (SFADE).
et. al., Swapnali Doley,
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A scalable framework for solving fractional diffusion equations [PDF]
Proceedings of the 34th ACM International Conference on Supercomputing, 2020 The study of fractional order differential operators is receiving renewed attention in many scientific fields. In order to accommodate researchers doing work in these areas, there is a need for highly scalable numerical methods for solving partial differential equations that involve fractional order operators on complex geometries. These operators have
Max Carlson +2 more
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On a Fractional Master Equation
International Journal of Differential Equations, 2011 A fractional order time-independent form of the wave equation or diffusion equation in two dimensions is obtained from the standard time-independent form of the wave equation or diffusion equation in two-dimensions by replacing the integer order partial ...
Anitha Thomas
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