The theory of functional connections, an analytical framework generalizing interpolation, was extended and applied in the context fractional-order operators (integrals derivatives). extension performed presented for univariate functions, with aim determining whole set functions satisfying some constraints expressed terms integrals derivatives non-integer order. objective these expressions to so...

Based on the local Shannon entropy concept in information theory, a new measure of aromaticity is introduced. This index, which describes the probability of electronic charge distribution between atoms in a given ring, is called Shannon aromaticity (SA). Using B3LYP method and different basis sets (6-31G**, 6-31+G** and 6-311++G**), the SA values of some five-membered heterocycles, C(4)H(4)X, a...

A new formulation of a pose refinement technique using “active” models is described. An error term derived from the detection of image derivatives close to an initial object hypothesis is linearised and solved by least squares. The method is particularly well suited to problems involving external geometrical constraints (such as the ground-plane constraint). We show that the method is able to r...

Four fundamental physical parameters of series of benzene derivatives were studied to ascertain correlations with biological activity. These included octanol/water coefficient, vapor pressure, infrared absorption (out-of-plane C-H vibration), and the pi values. Each physicochemical constant exhibited a partial correlation with biological activity suggesting that each played a role. It was presu...

The paper studies a model of fluid flow in fractured porous medium which fractures are distributed uniformly over the volume. This includes nonlinear equation containing several terms with fractional derivatives sense Caputo order belonging to interval 1,2. relevance studying this problem is determined by its practical significance oil industry, since most world’s reserves these types reservoir...

Some power series representations of the modified Bessel functions (McDonald functions Kα) are derived using the little known formalism of fractional derivatives. The resulting summation formulae are believed to be new. 1 Fractional derivatives There are several non-trivial examples in mathematics when some quantity, originally defined as integer, can radically extend its original range and ass...

Abstract In this article, analytical solutions of couple stress fluid flow modeled with a power law fractional differential operator are discussed. Stokes’ second problem for an incompressible is studied horizontal plate infinite length. The governing equations the expressed in terms partial and then converted into non-dimensional model by using dimensional analysis. Then integer order was form...

This study is devoted to constructing an approximate analytic solution of the fractional form a strongly nonlinear boundary value problem with multi-fractional derivatives that comes in chemical reactor theory. We construct algorithm based on generalized differential transform technique four simple steps. The derivative defined sense Caputo. also mathematically prove convergence algorithm. appl...

Acid-catalysed, '3+3' condensation of m-bispyrryl benzene derivatives with acetone afforded new non-aromatic macrocycles that can be converted to meso-alkylidenyl dibenzohexaphyrins carrying four exocyclic double bonds at meso-positions by DDQ oxidation.