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Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models
Essentials of Fractional Calculus Essentials of Linear Viscoelasticity Fractional Viscoelastic Media Waves in Linear Viscoelastic Media: Dispersion and Dissipation Waves in Linear Viscoelastic Media:Expand
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Fractional Calculus: Integral and Differential Equations of Fractional Order
We introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus. Particular attention is devoted to theExpand
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Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics
We review some applications of fractional calculus developed by the author (partly in collaboration with others) to treat some basic problems in continuum and statistical mechanics. The problems inExpand
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Mittag-Leffler Functions, Related Topics and Applications
As a result of researchers and scientists increasing interest in pure as well as applied mathematics in non-conventional models, particularly those using fractional calculus, Mittag-Leffler functionsExpand
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The fundamental solution of the space-time fractional diffusion equation
We deal with the Cauchy problem for the space-time fractional diffusion equation, which is obtained from the standard diffusion equation by replacing the second-order space derivative with aExpand
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Fractional Relaxation-Oscillation and Fractional Diffusion-Wave Phenomena
Abstract The processes involving the basic phenomena of relaxation, diffusion, oscillations and wave propagation are of great relevance in physics; from a mathematical point of view they are known toExpand
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The fundamental solutions for the fractional diffusion-wave equation
Abstract The time fractional diffusion-wave equation is obtained from the classical diffusion or wave equation by replacing the first- or second-order time derivative by a fractional derivative ofExpand
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On Mittag-Leffler-type functions in fractional evolution processes
Abstract We review a variety of fractional evolution processes (so defined being governed by equations of fractional order), whose solutions turn out to be related to Mittag-Leffler-type functions.Expand
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Creep, relaxation and viscosity properties for basic fractional models in rheology
Abstract.The purpose of this paper is twofold: from one side we provide a general survey to the viscoelastic models constructed via fractional calculus and from the other side we intend to analyzeExpand
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