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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New class of conformable derivatives and applications to differential impulsive systems
Yousef Gholami,Kazem Ghanbari +1 more
TL;DR: In this article, a new definition of conformable fractional derivatives and their algebraic properties are introduced, and the main tool of this establishment concerns with Lyapunov inequalities of under study fractional order linear systems.
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Nonlocal Probability Theory: General Fractional Calculus Approach
TL;DR: In this article , a nonlocal generalization of the standard probability theory based on the use of the general fractional calculus in the Luchko form is proposed, including nonlocal (general fractional) generalizations of probability density, cumulative distribution functions, probability, average values, and characteristic functions.
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Some Applications of Fractional Velocities
TL;DR: In this paper, the authors define fractional velocity as the limit of the difference quotient of the increments of a function and its argument raised to a fractional power, which is suitable for characterizing singular behavior of derivatives of Hölderian functions and non-differentiable functions.
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A derivative concept with respect to an arbitrary kernel and applications to fractional calculus
TL;DR: In this paper, a new concept of derivative with respect to an arbitrary kernel-function is proposed, and properties related to this new operator, like inversion rules, integration by parts, etc.
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A derivative concept with respect to an arbitrary kernel and applications to fractional calculus.
TL;DR: In this paper, a new concept of derivative with respect to an arbitrary kernel-function is proposed, and properties related to this new operator, like inversion rules, integration by parts, etc.
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.
Book
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
BookDOI
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.