No violation of the Leibniz rule. No fractional derivative
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It is proved that all fractional derivatives D α, which satisfy the Leibniz rule D α ( fg ) = ( D α f ) g + f ( D β g ) , should have the integer order α = 1.About:
This article is published in Communications in Nonlinear Science and Numerical Simulation.The article was published on 2013-11-01 and is currently open access. It has received 229 citations till now. The article focuses on the topics: General Leibniz rule & Leibniz integral rule.read more
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On the Cole–Hopf transformation and integration by parts formulae in computational methods within fractional differential equations and fractional optimal control theory:
TL;DR: The treatment of fractional differential equations and fractional optimal control problems is more difficult to tackle than the standard integer-order counterpart and may pose problems to non-speci....
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On the Validation of a Fractional Order Model for Pharmacokinetics Using Clinical Data
TL;DR: In this paper , two numerical methods, the Grunwald-Letnikov and the L1 approximation, were implemented for the two-compartment model with Michaelis-Menten clearance kinetics for oral and intravenous administration of the drug.
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All linear fractional derivatives with power functions’ convolution kernel and interpolation properties
Babak Shiri,Dumitru Baleanu +1 more
TL;DR: In this paper , the authors considered a special case of linear integro-differential operators with power functions' convolution kernel a(α)(t−s)b(α) of order α∈(0,1).
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Some Generalized Clifford-Jacobi Polynomials and Associated Spheroidal Wavelets
TL;DR: In this paper , the authors extend fractional calculus to the framework of cliffors analysis, and introduce wavelet functions based on 2-parameters weight functions, which extend the classical Jacobi ones in the context of Clifford analysis.
References
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Book
Theory and Applications of Fractional Differential Equations
TL;DR: In this article, the authors present a method for solving Fractional Differential Equations (DFE) using Integral Transform Methods for Explicit Solutions to FractionAL Differentially Equations.
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Fractional Integrals and Derivatives: Theory and Applications
TL;DR: Fractional integrals and derivatives on an interval fractional integral integrals on the real axis and half-axis further properties of fractional integral and derivatives, and derivatives of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations with special function kernels applications to differential equations as discussed by the authors.
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Applications Of Fractional Calculus In Physics
TL;DR: An introduction to fractional calculus can be found in this paper, where Butzer et al. present a discussion of fractional fractional derivatives, derivatives and fractal time series.
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Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models
TL;DR: The Eulerian Functions The Bessel Functions The Error Functions The Exponential Integral Functions The Mittag-Leffler Functions The Wright Functions as mentioned in this paper The Eulerians Functions
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Fractals and fractional calculus in continuum mechanics
TL;DR: Panagiotopoulos, O.K.Carpinteri, B. Chiaia, R. Gorenflo, F. Mainardi, and R. Lenormand as mentioned in this paper.