Document Type : Research Paper

Authors

• 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

Abstract

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.

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Keywords

• Calculus on Graphs
• Diffusion Equations
• Fractional Calculus