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
Citations
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Thermal properties of the one-dimensional space quantum fractional Dirac Oscillator
TL;DR: In this article , the authors investigated the fractional version of the one-dimensional relativistic oscillators and applied some important definitions and properties of a new kind of fractional formalism on the Dirac oscillator.
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Novel Investigation of Multivariable Conformable Calculus for Modeling Scientific Phenomena
TL;DR: In this article, the conformable version (CoV) of multivariable calculus is proposed and the CoV of implicit function theorem (IFThm) for SVs is established.
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Further Developments of Bessel Functions via Conformable Calculus with Applications
TL;DR: In this article, a conformable fractional-order Bessel functions (CFBFs) of the first kind were introduced and studied from different viewpoints, and several important formulas of the fractional Laplace Integral operator acting on the CFBFs were established.
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An introduction to fractional calculus: Numerical methods and application to HF dielectric response.
TL;DR: In this paper, the main concepts of fractional calculus are introduced, followed by one of its application to classical electrodynamics, illustrating how non-locality can be interpreted naturally in a fractional scenario.
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.
Book
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.
Book
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.