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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On the Thermal Properties of the One-Dimensional Space Fractional Duffin–Kemmer–Petiau Oscillator
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The Limited Validity of the Conformable Euler Finite Difference Method and an Alternate Definition of the Conformable Fractional Derivative to Justify Modification of the Method
TL;DR: In this paper, a modified conformable Euler method for the initial value problem is presented, based on the property of the conformable fractional derivative (CFD) used to show this limitation of the method, together with the integer definition of the derivative, and a method of constructing generalized derivatives from the solution of the non-integer relaxation equation is used to motivate an alternate definition of CFD and justify alternative generalizations of the Euler Method to CFD.
A bicomplex $(\vartheta,\varphi)-$weighted fractional Borel-Pompeiu type formula
TL;DR: In this paper , a Borel-Pompeiu type formula induced from a fractional bicomplex ( ϑ, ϕ ) − weighted Cauchy-Riemann operator was established.
Effect of local fractional derivatives on Riemann curvature tensor
TL;DR: In this article, the authors investigated the local fractional derivatives on the Riemann curvature tensor that is a common tool in cal-culating curvature of a Riemmannian manifold.
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The effect of Brownian motion and noise strength on solutions of stochastic Bogoyavlenskii model alongside conformable fractional derivative
TL;DR: In this paper , the authors obtained wave solutions of fractional order stochastic Bogoyavlenskii equation (SBE) in the viewpoint of stratonovich regarding multiplicative noise.
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
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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.