•Journal•ISSN: 1048-9533
Journal of Applied Mathematics and Stochastic Analysis
Hindawi Publishing Corporation
About: Journal of Applied Mathematics and Stochastic Analysis is an academic journal. The journal publishes majorly in the area(s): Differential equation & Nonlinear system. It has an ISSN identifier of 1048-9533. It is also open access. Over the lifetime, 641 publications have been published receiving 7314 citations.
Topics: Differential equation, Nonlinear system, Banach space, Uniqueness, Stochastic differential equation
Papers published on a yearly basis
Papers
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TL;DR: In this paper, the Sumudu transform is used to solve problems without resorting to a new frequency domain, which is the theoretical dual to the Laplace transform, and hence ought to rival it in problem solving.
Abstract: The Sumudu transform, whose fundamental properties are presented in this paper, is still not widely known, nor used. Having scale and unit-preserving properties, the Sumudu transform may be used to solve problems without resorting to a new frequency domain. In 2003, Belgacem et al. have shown it to be the theoretical dual to the Laplace transform, and hence ought to rival it in problem solving. Here, using the Laplace-Sumudu duality (LSD), we avail the reader with a complex formulation for the inverse Sumudu transform. Furthermore, we generalize all existing Sumudu differentiation, integration, and convolution theorems in the existing literature. We also generalize all existing Sumudu shifting theorems, and introduce new results and recurrence results, in this regard. Moreover, we use the Sumudu shift theorems to introduce a paradigm shift into the thinking of transform usage, with respect to solving differential equations, that may be unique to this transform due to its unit-preserving properties. Finally, we provide a large and more comprehensive list of Sumudu transforms of functions than is available in the literature.
299 citations
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TL;DR: In this article, an introduction to chaotic dynamical systems 2nd edition is given, which can be used as a starting point for a book reading session with a group of students.
Abstract: Imagine that you get such certain awesome experience and knowledge by only reading a book. How can? It seems to be greater when a book can be the best thing to discover. Books now will appear in printed and soft file collection. One of them is this book an introduction to chaotic dynamical systems 2nd edition. It is so usual with the printed books. However, many people sometimes have no space to bring the book for them; this is why they can't read the book wherever they want.
170 citations
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TL;DR: In this paper, the existence, uniqueness, and continuous dependence of a mild solution of a nonlocal Cauchy problem for a semilinear functional-differential evolution equation in a general Banach space are studied.
Abstract: The existence, uniqueness, and continuous dependence of a mild solution of a nonlocal Cauchy problem for a semilinear functional-differential evolution equation in a general Banach space are studied. Methods of a C0 semigroup of operators and the Banach contraction theorem are applied. The result obtained herein is a generalization and continuation of those reported in references [2-8].
146 citations
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Abstract: The mixed fractional Brownian motion is used in mathematical finance, in the modelling of some arbitrage-free and complete markets. In this paper, we present some stochastic properties and characteristics of this process, and we study the α-differentiability of its sample paths.
144 citations
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TL;DR: In this paper, a version of It's formula for fractional Brownian motion is derived for stochastic integrals with respect to FBM as an integrator if 1/2 < H < 1.
Abstract: Fractional Brownian motion (FBM) with Hurst index 1/2 < H < 1 is not a semimartingale. Consequently, the standard It calculus is not available for stochastic integrals with respect to FBM as an integrator if 1/2 < H < 1. In this paper we derive a version of It’s formula for fractional Brownian motion. Then, as an application, we propose and study a fractional Brownian Scholes stochastic model which includes the standard Black-Scholes model as a special case and is able to account for long range dependence in modeling the price of a risky asset.
140 citations