Related papers: Differential Calculus on Fuzzy Sphere and Scalar F…
In this paper presents the results obtained in the field of spectral theory operators of fractional differentiation. Proven a number of propositions which represents independent interest in the theory of fractional calculus. Introduced…
A fuzzy version of the ordinary round 2-sphere has been constructed with an invariant curvature. We here consider linear connections on arbitrary fuzzy surfaces of genus zero. We shall find as before that they are more or less rigidly…
We give a unified interpretation of confluences, contiguity relations and Katz's middle convolutions for linear ordinary differential equations with polynomial coefficients and their generalization to partial differential equations. The…
The magnetic Dirac operator describes the relativistic motion of a charged particle in a magnetic field. Although this operator got a lot of attention in physics many of its fundamental mathematical properties remain unexplored and this…
We create a sequence version of calculus. First, we define equivalence, some fundamental operations, differential, and integral for sequences. Then, we propose sequence versions of identity function, power function, exponential function,…
The Dirac wave function in a curved spacetime is usually defined as a quadruplet of scalar fields. It can alternatively be defined as a four-vector field. We describe these two representations in a common geometrical framework and we prove…
Considering the large number of fractional operators that exist, and since it does not seem that their number will stop increasing soon at the time of writing this paper, it is presented for the first time, as far as the authors know, a…
We establish the basis of a discrete function theory starting with a Fischer decomposition for difference Dirac operators. Discrete versions of homogeneous polynomials, Euler and Gamma operators are obtained. As a consequence we obtain a…
We introduce a fractional calculus on time scales using the theory of delta (or nabla) dynamic equations. The basic notions of fractional order integral and fractional order derivative on an arbitrary time scale are proposed, using the…
We address the computation of the determinant for the Dirac operator corresponding to a quark propagating in a background gluon field of the following type: the gauge field is covariantly constant and self-dual inside a hypersphere and with…
On this thesis we present the fuzzy sets, fuzzy numbers, the fractional derivative and also we discuss the solution of the first order of fuzzy hybrid equation.
We obtain explicit expressions for differential operators defining the action of the Virasoro algebra on the space of univalent functions. We also obtain an explicit Taylor decomposition for Schwarzian derivative and a formula for the…
We generalize the differential representation of the operators of the Galilean algebras to include fractional derivatives. As a result a whole new class of scale invariant Galilean algebras are obtained. The first member of this class has…
We present a formulation of chiral gauge theories, which admits more general spectra of Dirac operators and reveals considerably more possibilities for the structure of the chiral projections. Our two forms of correlation functions both…
We consider fractional differentiation operators in various senses and show that the strictly accretive property is the common property of fractional differentiation operators. Also we prove that the sectorial property holds for…
The slice Dirac operator over octonions is a slice counterpart of the Dirac operator over quaternions. It involves a new theory of stem functions, which is the extension from the commutative $ O(1) $ case to the non-commutative $ O(3) $…
We discuss a discrete analogue of the Dirac-K\"{a}hler equation in which chiral properties of the continual counterpart are captured. We pay special attention to a discrete Hodge star operator. To build one a combinatorial construction of…
We pose a new algebraic formalism for studying differential calculus in vector bundles. This is achieved by studying various functors of differential calculus over arbitrary graded commutative algebras (DCGCA) and applying this language to…
We discuss some of the mathematical properties of the fractional derivative defined by means of Fourier transforms. We first consider its action on the set of test functions $\Sc(\mathbb R)$, and then we extend it to its dual set,…
Many mathematical models utilize limit processes. Continuous functions and the calculus, differential equations and topology, all are based on limits and continuity. However, when we perform measurements and computations, we can achieve…