Titlebook: Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols; Sabir Umarov Book 2015 Springer International Publishi

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Pseudo-differential operators with singular symbols (,DOSS),in the dual variable. The presence of a singularity often causes a failure of well posedness of the problem in the sense of Hadamard. Let . be a linear differential operator mapping a function space . into another function space ..

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Fractional calculus and fractional order operators,ely reflect subtle internal properties, such as memory or hereditary properties, of complex processes that the classical integer order models neglect. In this chapter we will discuss the theoretical background of fractional modeling, that is the fractional calculus, including recent developments - d

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Boundary value problems for pseudo-differential equations with singular symbols,ferential and differential-operator equations of the form . where .(., .) is defined on . . and . are given functions; ..(.) and .., . are operators acting on some spaces (specified below) of functions defined on .; and . For example, when . the latter operators may act as .DOSS defined on the space

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https://doi.org/10.1007/978-3-319-20771-1Complex Fourier Transform; Fokker-Planck-Kolmogorov Equations; Fractional Differential Equations; Levy