Anomalous Diffusion Models Involving Regularized General Fractional Derivatives with Sonin Kernels
In this paper, we introduce a general fractional master equation involving regularized general fractional derivatives with Sonin kernels, and we discuss its physical characteristics and mathematical properties. First, we show that this master equation can be embedded into the framework of continuous...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-06-01
|
| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/9/6/363 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849472038006161408 |
|---|---|
| author | Maryam Alkandari Dimitri Loutchko Yuri Luchko |
| author_facet | Maryam Alkandari Dimitri Loutchko Yuri Luchko |
| author_sort | Maryam Alkandari |
| collection | DOAJ |
| description | In this paper, we introduce a general fractional master equation involving regularized general fractional derivatives with Sonin kernels, and we discuss its physical characteristics and mathematical properties. First, we show that this master equation can be embedded into the framework of continuous time random walks, and we derive an explicit formula for the waiting time probability density function of the continuous time random walk model in form of a convolution series generated by the Sonin kernel associated with the kernel of the regularized general fractional derivative. Next, we derive a fractional diffusion equation involving regularized general fractional derivatives with Sonin kernels from the continuous time random walk model in the asymptotical sense of long times and large distances. Another important result presented in this paper is a concise formula for the mean squared displacement of the particles governed by this fractional diffusion equation. Finally, we discuss several mathematical aspects of the fractional diffusion equation involving regularized general fractional derivatives with Sonin kernels, including the non-negativity of its fundamental solution and the validity of an appropriately formulated maximum principle for its solutions on the bounded domains. |
| format | Article |
| id | doaj-art-95c43b11fdfc43a2812dfe73a8fc5366 |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-95c43b11fdfc43a2812dfe73a8fc53662025-08-20T03:24:38ZengMDPI AGFractal and Fractional2504-31102025-06-019636310.3390/fractalfract9060363Anomalous Diffusion Models Involving Regularized General Fractional Derivatives with Sonin KernelsMaryam Alkandari0Dimitri Loutchko1Yuri Luchko2Department of Mathematics, Kuwait University, Kuwait City 13060, KuwaitInstitute of Industrial Science, The University of Tokyo, Tokyo 153-8505, JapanDepartment of Mathematics, Physics, and Chemistry, Berlin University of Applied Sciences and Technology, 13353 Berlin, GermanyIn this paper, we introduce a general fractional master equation involving regularized general fractional derivatives with Sonin kernels, and we discuss its physical characteristics and mathematical properties. First, we show that this master equation can be embedded into the framework of continuous time random walks, and we derive an explicit formula for the waiting time probability density function of the continuous time random walk model in form of a convolution series generated by the Sonin kernel associated with the kernel of the regularized general fractional derivative. Next, we derive a fractional diffusion equation involving regularized general fractional derivatives with Sonin kernels from the continuous time random walk model in the asymptotical sense of long times and large distances. Another important result presented in this paper is a concise formula for the mean squared displacement of the particles governed by this fractional diffusion equation. Finally, we discuss several mathematical aspects of the fractional diffusion equation involving regularized general fractional derivatives with Sonin kernels, including the non-negativity of its fundamental solution and the validity of an appropriately formulated maximum principle for its solutions on the bounded domains.https://www.mdpi.com/2504-3110/9/6/363anomalous diffusioncontinuous time random walksfractional master equationregularized general fractional derivativeSonin kernelsfractional diffusion equation |
| spellingShingle | Maryam Alkandari Dimitri Loutchko Yuri Luchko Anomalous Diffusion Models Involving Regularized General Fractional Derivatives with Sonin Kernels Fractal and Fractional anomalous diffusion continuous time random walks fractional master equation regularized general fractional derivative Sonin kernels fractional diffusion equation |
| title | Anomalous Diffusion Models Involving Regularized General Fractional Derivatives with Sonin Kernels |
| title_full | Anomalous Diffusion Models Involving Regularized General Fractional Derivatives with Sonin Kernels |
| title_fullStr | Anomalous Diffusion Models Involving Regularized General Fractional Derivatives with Sonin Kernels |
| title_full_unstemmed | Anomalous Diffusion Models Involving Regularized General Fractional Derivatives with Sonin Kernels |
| title_short | Anomalous Diffusion Models Involving Regularized General Fractional Derivatives with Sonin Kernels |
| title_sort | anomalous diffusion models involving regularized general fractional derivatives with sonin kernels |
| topic | anomalous diffusion continuous time random walks fractional master equation regularized general fractional derivative Sonin kernels fractional diffusion equation |
| url | https://www.mdpi.com/2504-3110/9/6/363 |
| work_keys_str_mv | AT maryamalkandari anomalousdiffusionmodelsinvolvingregularizedgeneralfractionalderivativeswithsoninkernels AT dimitriloutchko anomalousdiffusionmodelsinvolvingregularizedgeneralfractionalderivativeswithsoninkernels AT yuriluchko anomalousdiffusionmodelsinvolvingregularizedgeneralfractionalderivativeswithsoninkernels |