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Fractional differential equations thesis

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Su Yang , University of South Carolina. In physical point of view, relaxation usually describes the return from a perturbed system into equilibrium and each process has its own characteristic relaxation time. In , Tool first formulated the notion of fictive temperature to characterize the structure of a glass-forming melt. Since then, people used to simulate structural relaxation by first order model. Since fractional-based models have not widely applied in modeling the fictive temperature, I want to explore the the possibility of modeling structural relaxation by fractional differential equation.

Fractional Differential Equations

An application of fractional differential equations to risk theory | SpringerLink

Fractional differential equations can describe the dynamics of several complex and nonlocal systems with memory. They arise in many scientific and engineering areas such as physics, chemistry, biology, biophysics, economics, control theory, signal and image processing, etc. Particularly, nonlinear systems describing different phenomena can be modeled with fractional derivatives. Chaotic behavior has also been reported in some fractional models.

Fractional calculus

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