Fractional Order Systems and Applications in Engineering

Chapter 3: Analytical solutions of some fractional diffusion boundary value problems

Trilok Mathur^a; Shivi Agarwal^a; S.P. Goyal^b; K. Satya Pritam^c    aDepartment of Mathematics, Birla Institute of Technology and Science, Pilani, India^bDepartment of Mathematics, University of Rajasthan, Jaipur, India^cDepartment of Mathematics, Pandit Deendayal Petroleum University, Gandhinagar, India

Abstract

Adolf Fick gave a simple description of diffusion in the 19th century. In usual Fickian diffusion, there is a flow from a high concentration level to a low concentration level, where the Gaussian distribution describes the concentration, and asymptotical mean-squared displacement is as a linear function of time. The model is described by integer-order partial ...