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TEMPERED FRACTIONAL CALCULUS. [PDF]
J Comput Phys, 2015 Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an ...
Meerschaert MM, Sabzikar F, Chen J.
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Fractional calculus in pharmacokinetics [PDF]
Journal of Pharmacokinetics and Pharmacodynamics, 2017 We are witnessing the birth of a new variety of pharmacokinetics where non-integer-order differential equations are employed to study the time course of drugs in the body: this is dubbed "fractional pharmacokinetics." The presence of fractional kinetics has important clinical implications such as the lack of a half-life, observed, for example with the ...
Pantelis Sopasakis +3 more
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On Weyl fractional calculus [PDF]
Proceedings of the American Mathematical Society, 1979 The Weyl fractional calculus is applied in developing the Laplace transform of t q f ( t ) {t^q}f(t) , for all values of q. Also, a generalized Taylor’s formula in Weyl fractional calculus is established.
Raina, R. K., Koul, C. L.
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Fractional-calculus diffusion equation [PDF]
Nonlinear Biomedical Physics, 2010 Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems.The canonical quantization of a system represented classically by one-dimensional Fick's law, and the ...
Ajlouni, Abdul-Wali M. S. +1 more
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Fractional Calculus and Shannon Wavelet [PDF]
Mathematical Problems in Engineering, 2012 An explicit analytical formula for the any order fractional derivative of Shannon wavelet is given as wavelet series based on connection coefficients. So that for any L2(ℝ) function, reconstructed by Shannon wavelets, we can easily define its fractional derivative.
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Fractional vector calculus and fractional Maxwell’s equations [PDF]
Annals of Physics, 2008 The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper.
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Multi-variable conformable fractional calculus
Filomat, 2018 Conformable fractional derivative is introduced by the authors Khalil et al. In this study we develop their concept and introduce multi-variable conformable derivative for a vector valued function with several ...
Gözütok, Nazlı Yazıcı +1 more
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Fractional Tempered Variational Calculus
Mathematical Methods in the Applied SciencesABSTRACTIn this paper, we derive sufficient conditions ensuring the existence of a weak solution for a tempered fractional Euler‐Lagrange equations. Furthermore, we study a fractional tempered version of Noether theorem, and we provide a very explicit expression of a constant of motion in terms of symmetry group and Lagrangian for fractional problems
César E. Torres Ledesma +3 more
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Fractional calculus in mathematical oncology. [PDF]
Sci Rep, 2023 Alinei-Poiana T, Dulf EH, Kovacs L.
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