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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Intrinsic Discontinuities in Solutions of Evolution Equations Involving Fractional Caputo–Fabrizio and Atangana–Baleanu Operators
TL;DR: In this paper, the authors present solutions to simple initial value problems involving the Atangana-Baleanu operator and the Caputo-Fabrizio operator with intrinsic discontinuity at the origin.
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Local Fractional Derivatives of Differentiable Functions are Integer-order Derivatives or Zero
TL;DR: In this paper, it was shown that the local fractional derivatives of differentiable functions are integer-order derivatives or zero operator, and the requirement of the existence of integer order derivatives allows us to conclude that the Local fractional derivative cannot be considered as the best method to describe nowhere differentiable function and fractal objects.
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Output feedback consensus control for fractional-order nonlinear multi-agent systems with directed topologies
Ping Gong,Kun Wang +1 more
TL;DR: By introducing a distributed filter for each agent, a control algorithm that uses only relative position measurements is proposed to guarantee the global leaderless consensus can be achieved.
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A new glance on the Leibniz rule for fractional derivatives
TL;DR: The results demonstrate that the proposed theoretical analysis of the Leibniz rule for fractional derivatives is accurate.
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Mathematical analysis of a power-law form time dependent vector-borne disease transmission model.
Tridip Sardar,Bapi Saha +1 more
TL;DR: A general time dependent single strain vector borne disease model is derived and it is shown that under certain choice of time dependent transmission kernel this model can be converted into the classical integer order system.
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.