The key purpose of the present work is to constitute a numerical algorithm based on fractional homotopy analysis transform method to study the fractional model of Lienard’s equations. The Lienard’s ...equation describes the oscillating circuits. The suggested scheme is a merger of homotopy analysis technique, classical Laplace transform and homotopy polynomials. The uniqueness and convergence analysis of the solution are also discussed. The numerical and graphical results elucidate that the suggested approach is very straightforward and accurate.
We introduce and study the homotopy theory of motivic spaces and spectra parametrized by quotient stacks X/G, where G is a linearly reductive linear algebraic group. We extend to this equivariant ...setting the main foundational results of motivic homotopy theory: the (unstable) purity and gluing theorems of Morel–Voevodsky and the (stable) ambidexterity theorem of Ayoub. Our proof of the latter is different than Ayoub's and is of interest even when G is trivial. Using these results, we construct a formalism of six operations for equivariant motivic spectra, and we deduce that any cohomology theory for G-schemes that is represented by an absolute motivic spectrum satisfies descent for the cdh topology.
Equivariant homotopy theory started from geometrically motivated questions about symmetries of manifolds. Several important equivariant phenomena occur not just for a particular group, but in a ...uniform way for all groups. Prominent examples include stable homotopy, K-theory or bordism. Global equivariant homotopy theory studies such uniform phenomena, i.e. universal symmetries encoded by simultaneous and compatible actions of all compact Lie groups. This book introduces graduate students and researchers to global equivariant homotopy theory. The framework is based on the new notion of global equivalences for orthogonal spectra, a much finer notion of equivalence than is traditionally considered. The treatment is largely self-contained and contains many examples, making it suitable as a textbook for an advanced graduate class. At the same time, the book is a comprehensive research monograph with detailed calculations that reveal the intrinsic beauty of global equivariant phenomena.
The Black - Scholes Model is commonly used for option pricing, which is one of the most important applications in finance. In the absence of a transaction cost, the value of the option is determined ...by using B-S model. In the view of Caputo sense, this study proposes a result for the fractional Black-Scholes equation (FBSE) problem. The main goal of this paper is to show how to solve the FBSE by a semi-analytical method called the homotopy analysis shehu transform method (HASTM) and compare that homotopy analysis method (HAM), homotopy perturbation method (HPM), elzaki transform homotopy perturbation method (ETHPM). The HASTM result is quite similar to the HAM, HPM, ETHPM solution. The HASTM and other methods analytical solutions are also represented.
Higher topos theory Lurie, Jacob; Lurie, Jacob
2009., 20090706, 2009, 2009-07-06, Letnik:
170
eBook
Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher ...morphisms are assumed to be invertible. In Higher Topos Theory, Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language. The result is a powerful theory with applications in many areas of mathematics.
In this paper, numerical solution of the mathematical model describing the deathly disease in pregnant women with fractional order is investigated with the help of q-homotopy analysis transform ...method (q-HATM). This sophisticated and important model is consisted of a system of four equations, which illustrate a deathly disease spreading pregnant women called Lassa hemorrhagic fever disease. The fixed point theorem is considered so as to demonstrate the existence and uniqueness of the obtained numerical solution for the governing fractional model. The proposed method is also included the Laplace transform technique with q-homotopy analysis scheme, and fractional derivative defined with Atangana-Baleanu (AB) operator. In order to illustrate and validate the efficiency of the future technique, the projected model in the sense of fractional order is also considered. Moreover, the physical behaviors of the obtained numerical results are presented in terms of simulations for diverse fractional order.
In this paper, we present a new definition of fractional-order derivative with a smooth kernel based on the Caputo–Fabrizio fractional-order operator which takes into account some problems related ...with the conventional Caputo–Fabrizio factional-order derivative definition. The Modified-Caputo–Fabrizio fractional-order derivative here introduced presents some advantages when some approximated analytical methods are applied to solve non-linear fractional differential equations. We consider two approximated analytical methods to find analytical solutions for this novel operator; the homotopy analysis method (HAM) and the multi step homotopy analysis method (MHAM). The results obtained suggest that the introduction of the Modified-Caputo–Fabrizio fractional-order derivative can be applied in the future to many different scenarios in fractional dynamics.
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