Related papers: Generalized second-order partial derivatives of 1/…
By using generalized fractional derivative, the parametric generalized fractional Nikiforov-Uvarov (NU) method is introduced. The second-order parametric generalized differential equation is exactly solved in the fractional form. The…
Complex-linearization of a class of systems of second order ordinary differential equations (ODEs) has already been studied with complex symmetry analysis. Linearization of this class has been achieved earlier by complex method, however,…
The goal of this communication is to propose a generalized notion of the "traditional derivative". This generalization includes the fractional derivatives such as the Riemann-Liouville, Gruenwald-Letnikov, Weyl, Riesz, Caputo, Marchaud…
We generalize the spherical harmonics for l=1 and give the differential equation that the generalized forms satisfy. The new forms have an obvious interpretation in the context of quantum mechanics.
We show that a form for the second partial derivative of $1/r$ proposed by Frahm and subsequently used by other workers applies only when averaged over smooth functions. We use dyadic notation to derive a more general form without that…
The derivative expansion of the effective action is considered in the model with two interacting real scalar fields in curved spacetime. Using the functional approach and local momentum representation, the coefficient of the derivative term…
Introducing certain singularities, we generalize the class of one-dimensional stochastic differential equations with so-called generalized drift. Equations with generalized drift, well-known in the literature, possess a drift that is…
The "marginal" distributions for measurable coordinate and spin projection is introduced. Then, the analog of the Pauli equation for spin-1/2 particle is obtained for such probability distributions instead of the usual wave functions. That…
The question of defining unique, generally applicable constrained second, and higher-order, derivatives is investigated. It is shown that second-order constrained derivatives obtained via two successive constrained differentiations provide…
Using the elementary axioms of special relativity and quantum mechanics we construct a wave equation which generalizes the Schrodinger equation. We also solve the general second and some higher order differential equations.
Two approximations, derived from continuous expansions of Riemann-Liouville fractional derivatives into series involving integer order derivatives, are studied. Using those series, one can formally transform any problem that contains…
This paper develops one of the methods for study of nonlinear Partial Differential equations. We generalize Sato equation and represent the algorithm for construction of some classes of nonlinear Partial Differential Equations (PDE)…
We consider a fractional generalization of gradient systems. We use differential forms and exterior derivatives of fractional orders. Examples of fractional gradient systems are considered. We describe the stationary states of these…
The transformation of the partial fractional derivatives under spatial rotation in $R^2$ are derived for the Riemann-Liouville and Caputo definitions. These transformation properties link the observation of physical quantities, expressed…
We discuss the mechanism through which classicalization may occur during the collapse of a spherical field configuration modelled as a wavepacket. We demonstrate that the phenomenon is associated with the dynamical change of the equation of…
A method of calculation for the variational derivatives for gravitational actions in the pseudo-Riemannian case is proposed as a practical variant of the first order formalism with constraints. The method is then used to derive the metric…
We establish a new generalized Taylor's formula for power fractional derivatives with nonsingular and nonlocal kernels, which includes many known Taylor's formulas in the literature. Moreover, as a consequence, we obtain a general version…
A new discretization of the radial equations that appear in the solution of separable second order partial differential equations with some rotational symmetry (as the Schrodinger equation in a central potential) is presented. It cures a…
Generalized dualities had an intriguing incursion into Double Field Theory (DFT) in terms of local $O(d,d)$ transformations. We review this idea and use the higher derivative formulation of DFT to compute the first order corrections to…
The paper is mainly devoted to systematic developments and applications of geometric aspects of second-order variational analysis that are revolved around the concept of parabolic regularity of sets. This concept has been known in…