Fractional Differential Equations: Theoretical Aspects and Applications

Fractional Differential Equations: Theoretical Aspects and Applications presents the latest mathematical and conceptual developments in the field of Fractional Calculus and explores the scope of applications in research science and computational modelling. Fractional derivatives arise as a generalization of integer order derivatives and have a long history: their origin can be found in the work of G. W. Leibniz and L. Euler. Shortly after being introduced, the new theory turned out to be very attractive for many famous mathematicians and scientists, including P. S. Laplace, B. Riemann, J. Liouville, N. H. Abel, and J. B. J. Fourier, due to the numerous possibilities it offered for applications.

Fractional Calculus, the field of mathematics dealing with operators of differentiation and integration of arbitrary real or even complex order, extends many of the modelling capabilities of conventional calculus and integer-order differential equations and finds its application in various scientific areas, such as physics, mechanics, engineering, economics, finance, biology, and chemistry, among others. However, many aspects from the theoretical and practical point of view have still to be developed in relation with models based on fractional operators. Efficient analytical and numerical methods have been developed but still need particular attention. Fractional Differential Equations: Theoretical Aspects and Applications delves into these methods and applied computational modelling techniques, including analysis of equations involving fractional derivatives, fractional derivatives and the wave equation, analysis of FDE on groups, direct and inverse problems, functional inequalities, and computational methods for FDEs in physics and engineering. Other modelling techniques and applications explored by the authors include general fractional derivatives involving the special functions in analysis, fractional derivatives with respect to another function in analysis, new fractional operators in real-world applications, fractional order dynamical systems, hidden attractors in complex systems, nonlinear dynamics and chaos in engineering applications, quantum chaos, and self-excited attractors.