Fractional Differential Equations in Anomalous Diffusion

Dear Colleagues,

The phenomenon of anomalous diffusion is an important dynamic behavior arising from many applied science fields, such as turbulence, (see page on porous media and pollution control). Thus, nonlinear modelling is a better strategy to depict a variety of complex anomalous diffusion phenomena. However, modelling anomalous diffusion using the differential equation is still a perplexing mathematical physics issue. Because the fractal or the fractional derivative can well describe the inherent abnormal-exponential or heavy-tail decay processes, in recent decades fractal and fractional derivatives have been used to model many anomalous diffusion processes.

Thus, fractional differential equation in anomalous diffusion has become a new research area of analytical mathematics, providing useful tools to model many problems arising from mathematical physics, fluid dynamics, chemistry, biology, economics, control theory and image processing with memory effects.

We invite researchers to submit original research as well as review articles discussing the recent development of the fractional differential equation in anomalous diffusion and its applications in sciences, technologies and engineering.

Topics include (but are not limited to):

• Theory of the fractal or the fractional derivative.
• Initial and boundary value problems of fractional differential equations in anomalous diffusion.
• Inequalities of fractional integrals and fractional derivatives.
• Singular and impulsive fractional differential and integral equations.
• Analysis and control in the fractal or the fractional differential equations with anomalous diffusion.
• Numerical analysis and algorithm for fractional differential equations.
• Fixed point theory and application in fractional calculus.
• Fractional functional equations in function spaces.
• Fractional network arising in physical models.
• Fractional stochastic differential equations.

Dr. Xinguang Zhang
Prof. Dr. Yonghong Wu
Prof. Dr. Chuanjun Chen
Dr. Jiwei Zhang
Dr. Chun Lu
Guest Editors

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