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Mainardi F. (Ed.) Fractional Calculus: Theory and Applications

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Mainardi F. (Ed.) Fractional Calculus: Theory and Applications
Basel, Switzerland: MDPI, 2018. — 210 p. — ISBN 3038972061.
Fractional calculus is allowing integrals and derivatives of any positive order (the term fractional is kept only for historical reasons). It can be considered a branch of mathematical physics that deals with integro-differential equations, where integrals are of convolution type and exhibit mainly singular kernels of power law or logarithm type.
It is a subject that has gained considerably popularity and importance in the past few decades in diverse fields of science and engineering. Efficient analytical and numerical methods have been developed but still need particular attention.
The purpose of this Special Issue is to establish a collection of articles that reflect the latest mathematical and conceptual developments in the field of fractional calculus and explore the scope for applications in applied sciences.
Contents
Fractional Calculus: Theory and Applications
A Note on the Equivalence of Fractional Relaxation Equations to Differential Equations with Varying Coefficients
Weyl and Marchaud Derivatives: A Forgotten History
Letnikov vs. Marchaud: A Survey on Two ProminentConstructions of Fractional Derivatives
Generalized Langevin Equation and the Prabhakar Derivative
A Note on Hadamard Fractional Differential Equations with Varying Coefficients and Their Applications in Probability
On Some New Properties of the Fundamental Solution to the Multi-Dimensional Space- and Time-Fractional Diffusion-Wave Equation
An Iterative Method for Solving a Class of Fractional Functional Differential Equations with
“Maxima”
Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial
Numerical Solution of Multiterm Fractional Differential Equations Using the Matrix Mittag–Leffler Functions
Best Approximation of the Fractional Semi-Derivative Operator by Exponential Series
Storage and Dissipation of Energy in Prabhakar Viscoelasticity
Fractional Derivatives, Memory Kernels and Solution of a Free Electron Laser Volterra Type Equation
Application of Tempered-Stable Time Fractional-Derivative Model to Upscale Subdiffusion for Pollutant Transport in Field-Scale Discrete Fracture Networks
Analysis of PFG Anomalous Diffusion via Real-Space and Phase-Space Approaches
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