A model for computing image ow in image sequences containing a very wide range of instantaneous ows is proposed. This model integrates the spatio-temporal image derivatives from multiple temporal scales to provide both reliable and accurate instantaneous ow estimates. The integration employs robust regression and automatic scale weighting in a generalized brightness constancy framework. In addi...

This paper presents a self-contained new theory of weak fractional differential calculus in one-dimension. The crux this is the introduction derivative notion which natural generalization integer order derivatives; it also helps to unify multiple existing definitions and characterize what functions are fractionally differentiable. Various rules including fundamental theorem calculus, product ch...

The continuous wavelet transform has been used with much success in the analysis of non-stationary time series. It has been used much less frequently in the interpretation of magnetic or gravity data, although several approaches have been tried. A simple method of obtaining location and depth estimates of gravity and magnetic field sources is suggested here. For gravity data the method uses wav...

The relation showing that the Grünwald-Letnikov and generalised Cauchy derivatives are equal is presented. This establishes a bridge between two different formulations and simultaneously between the classic integer order derivatives and the fractional ones. Starting from the generalised Cauchy derivative formula, new relations are obtained, namely a regularised version that makes the concept of...

In the last few decades many authors pointed out that derivatives and integrals of non-integer order are very suitable for description properties various real problems. It has been shown fractional-order models more adequate than previously used integer-order models. this work, we aim to investigate different features plant virus model with its fractional equivalent. We present an application r...

Derivatives and integrals of non-integer orders have a wide application to describe complex properties of physical systems and media including nonlocality of power-law type and long-term memory. We suggest an extension of the standard variational principle for fractional nonlocal media with power-law type nonlocality that is described by the Riesz-type derivatives of non-integer orders. As exam...

We consider a massless higher spin field theory within the BRST approach and construct general off-shell cubic vertex corresponding to irreducible fields of helicities $s_1, s_2, s_3$. Unlike previous works on vertices, which do not take into account trace constraints, we use complete operator, including constraints that describe an representation with definite integer helicity. As result, gene...

This communication addresses a comparison of newly presented non-integer order derivatives with and without singular kernel, namely Michele Caputo–Mauro Fabrizio (CF) CF(∂β/∂tβ) and Atangana–Baleanu (AB) AB(∂α/∂tα) fractional derivatives. For this purpose, second grade fluids flow with combined gradients of mass concentration and temperature distribution over a vertical flat plate is considered...

Derivatives and integrals of non-integer order were introduced more than three centuries ago, but only recently gained more attention due to their application on nonlocal phenomena. In this context, the Caputo derivatives are the most popular approach to fractional calculus among physicists, since differential equations involving Caputo derivatives require regular boundary conditions. Motivated...

Meromorphic solutions of non-linear differential equations the form f n + P ( z , ) = h are investigated, where ? 2 is an integer, a meromorphic function, and polynomial in its derivatives with small functions as coefficients. In existing literature this equation has been studied case when particular p 1 e ? entire functions. such order either positive integer or equal to infinity. article it a...