A new mathematical model of Coronavirus (2019-nCov) using piecewise hybrid fractional order derivatives is given in this paper. Moreover, to be consistent with the physical problem, a parameter ? presented. The boundedness, existence, and positivity solutions for proposed are discussed. Two improved numerical methods presented Caputo proportional constant nonstandard modified Euler–Maruyama met...

Formulation of locally conservative least-squares finite element methods (LSFEM) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require nonstandard boundary conditions [3], while methods that admit the no-slip condition satisfy the incompressibility equation only approximately [4, Chapt...

Abstract We propose a new theory based on the notions of marginal and large difference which has natural models in context nonstandard mathematics. introduce notion finite marginality show representation result ensures, for finitely countable models, existence homomorphism structure into model numbers, extent to any such is unique. Finally, we that our constitutes part underlying abstract three...

We studied oscillatory behavior of critical amplitudes for the Gaussian model on a hierarchical structure presented by a modified Sierpinski gasket lattice. This model is known to display nonstandard critical behavior on the lattice under study. The leading singular behavior of the correlation length xi near the critical coupling K=K(c) is modulated by a function which is periodic in ln/ln(K(c)...

This paper describes a type constructor for nonstandard extensions of arbitrary types, generalizing the previous formalization of nonstandard analysis in Isabelle by Fleuriot and Paulson [1]. In addition to numeric types, nonstandard extensions of function spaces and set types also prove useful—they provide an elegant way to define internal functions and internal sets. The paper also describes ...

In this paper, we introduce systems of nonstandard second-order arithmetic which are conservative extensions of systems of second-order arithmetic. Within these systems, we do reverse mathematics for nonstandard analysis, and we can import techniques of nonstandard analysis into analysis in weak systems of second-order arithmetic. Then, we apply nonstandard techniques to a version of Riemann’s ...

We present and compare various types of discretizations which have been proposed to approximate the total variation (mostly, a gray-level image in two dimensions). discuss properties finite differences elements based approach their merits, particular terms error estimates quality reconstruction.