منابع مشابه
SOME APPLICATIONS OF FRACTIONAL q-CALCULUS AND FRACTIONAL q-LEIBNIZ RULE
In this article, the fractional q-calculus and fractional q-Leibniz rule are used to generate certain infinite series expansions and transformations relating some of q-special functions of mathematical physics. Some of these expansions and transformations thus generated are known, while others appear to be new.
متن کاملFractional Dynamical Systems on Fractional Leibniz Algebroids
The theory of derivative of noninteger order goes back to Leibniz, Liouville, Riemann, Grunwald and Letnikov. Derivatives of fractional order have found many applications in recent studies in mechanics, physics, economics, medicine.Classes of fractional differentiable systems have studied in [10], [4]. In the first section the fractional tangent bundle to a differentiable manifold is defined, u...
متن کاملOn The Leibniz Rule And Fractional Derivative For Differentiable And Non-Differentiable Functions
In the recent paper Communications in Nonlinear Science and Numerical Simulation. Vol.18. No.11. (2013) 2945-2948, it was demonstrated that a violation of the Leibniz rule is a characteristic property of derivatives of non-integer orders. It was proved that all fractional derivatives Dα, which satisfy the Leibniz rule Dα(fg) = (Dαf) g+ f (Dαg), should have the integer order α = 1, i.e. fraction...
متن کاملHigher Order Refinement Heuristics for Rule Validation
For rule validation there are no second and higher order refinement heuristics yet. This paper presents an example for second order refinement heuristics and introduces generic higher order refinement heuristics. It is proposed that rule refinement should be performed case-based, i.e. the whole spectrum from first order to higher order refinement heuristics can be processed instead of first ord...
متن کاملTaming the Leibniz Rule on the Lattice
We study a product rule and a difference operator equipped with Leibniz rule in a general framework of lattice field theory. It is shown that the difference operator can be determined by the product rule and some initial data through the Leibniz rule. This observation leads to a no-go theorem that it is impossible to construct any difference operator and product rule on a lattice with the prope...
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ژورنال
عنوان ژورنال: Journal of Fourier Analysis and Applications
سال: 2017
ISSN: 1069-5869,1531-5851
DOI: 10.1007/s00041-017-9541-y