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Existence of solutions for time fractional order diffusion equations on weighted graphs | ||
International Journal of Nonlinear Analysis and Applications | ||
مقاله 179، دوره 13، شماره 2، مهر 2022، صفحه 2219-2232 اصل مقاله (1.1 M) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23258.2511 | ||
نویسندگان | ||
Kaninpat Wattanagul؛ Parinya Sa Ngiamsunthorn* | ||
Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, 126 Pracha Uthit Road, Bang Mod, Thung Kru, Bangkok, 10140, Thailand | ||
تاریخ دریافت: 06 اردیبهشت 1400، تاریخ بازنگری: 04 مهر 1400، تاریخ پذیرش: 22 مهر 1400 | ||
چکیده | ||
We generalize the concept of diffusion equations on weighted graphs, which is also known as $\omega$-diffusion equations, to study fractional order diffusion equations on weighted graphs. More precisely, we replace the ordinary first order derivative in time by a fractional derivative of order $\alpha$ in the sense of Riemann-Liouville and Caputo fractional derivatives. We prove the existence of solutions of fractional order diffusion equations on graphs using the concept of $\alpha$-exponential matrix and illustrate the solutions through numerical simulation in various examples. | ||
تازه های تحقیق | ||
[1] P. Agarwal and J.E. Restrepo, An extension by means of ω-weighted classes of the generalized Riemann-Liouville | ||
کلیدواژهها | ||
Calculus on Graphs؛ Diffusion Equations؛ Fractional Calculus | ||
مراجع | ||
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