1,720,978 research outputs found
Existence, Uniqueness and Ulam’s Stability of Solutions for a Coupled System of Fractional Differential Equations with Integral Boundary Conditions
No full textIn this paper, the existence and uniqueness of the solutions to a fractional order nonlinear coupled system with integral boundary conditions is investigated. Furthermore, Ulam’s type stability of the proposed coupled system is studied. Banach’s fixed point theorem is used to obtain the existence and uniqueness of the solutions. Finally, an example is provided to illustrate the analytical findings
Optimal Control for Neutral Stochastic Integrodifferential Equations with Infinite Delay Driven by Poisson Jumps and Rosenblatt Process
No full textIn this paper, we investigate the optimal control problems for a class of neutral stochastic integrodifferential equations (NSIDEs) with infinite delay driven by Poisson jumps and the Rosenblat process in Hilbert space involving concrete-fading memory-phase space, in which we define the advanced phase space for infinite delay for the stochastic process. First, we introduce conditions that ensure the existence and uniqueness of mild solutions using stochastic analysis theory, successive approximation, and Grimmer’s resolvent operator theory. Next, we prove exponential stability, which includes mean square exponential stability, and this especially includes the exponential stability of solutions and their maps. Following that, we discuss the existence requirements of an optimal pair of systems governed by stochastic partial integrodifferential equations with infinite delay. Then, we explore examples that illustrate the potential of the main result, mainly in the heat equation, filter system, traffic signal light systems, and the biological processes in the human body. We conclude with a numerical simulation of the system studied. This work is a unique combination of the theory with practical examples and a numerical simulation
Correction: Thabet, H.; Kendre, S.; Chalishajar, D. New Analytical Technique for Solving a System of Nonlinear Fractional Partial Differential Equations Mathematics 2017, 5, 47
No full textWe have found some errors in the caption of Figure 1 and Figure 2 in our paper [1], and thus would like to make the following corrections:[...
Existence of Semi Linear Impulsive Neutral Evolution Inclusions with Infinite Delay in Frechet Spaces
No full textIn this paper, sufficient conditions are given to investigate the existence of mild solutions on a semi-infinite interval for first order semi linear impulsive neutral functional differential evolution inclusions with infinite delay using a recently developed nonlinear alternative for contractive multivalued maps in Frechet spaces due to Frigon combined with semigroup theory. The existence result has been proved without assumption of compactness of the semigroup. We introduced a new phase space for impulsive system with infinite delay and claim that the phase space considered by different authors are not correct
Asymptotic Behavior of Solutions of the Third Order Nonlinear Mixed Type Neutral Differential Equations
No full textThe objective of our paper is to study asymptotic properties of the class of third order neutral differential equations with advanced and delayed arguments. Our results supplement and improve some known results obtained in the literature. An illustrative example is provided
Armstrong Calculus
Get PDFoai:oer.galileo.usg.edu:mathematics-textbooks-1000Authors\u27 Description:
An open-source textbook for calculus.
The text is mostly an adaptation of two other excellent open- source calculus textbooks: Active Calculus by Dr. Matt Boelkins of Grand Valley State University and Drs. Gregory Hartman, Brian Heinold, Troy Siemers, Dimplekumar Chalishajar, and Jennifer Bowen of the Virginia Military Institute and Mount Saint Mary\u27s University. Both of these texts can be found at http://aimath.org/textbooks/approved-textbooks/.
The authors of this text have combined sections, examples, and exercises from the above two texts along with some of their own content to generate this text. The impetus for the creation of this text was to adopt an open-source textbook for Calculus while maintaining the typical schedule and content of the calculus sequence at our home institution.
Accessible files with optical character recognition (OCR) and auto-tagging provided by the Center for Inclusive Design and Innovation.https://oer.galileo.usg.edu/mathematics-textbooks/1000/thumbnail.jp
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
New Analytical Technique for Solving a System of Nonlinear Fractional Partial Differential Equations
No full textThis paper introduces a new analytical technique (NAT) for solving a system of nonlinear fractional partial differential equations (NFPDEs) in full general set. Moreover, the convergence and error analysis of the proposed technique is shown. The approximate solutions for a system of NFPDEs are easily obtained by means of Caputo fractional partial derivatives based on the properties of fractional calculus. However, analytical and numerical traveling wave solutions for some systems of nonlinear wave equations are successfully obtained to confirm the accuracy and efficiency of the proposed technique. Several numerical results are presented in the format of tables and graphs to make a comparison with results previously obtained by other well-known methods
Some Qualitative Behavior of Solutions of General Class of Difference Equations
No full textIn this work, we consider the general class of difference equations (covered many equations that have been studied by other authors or that have never been studied before), as a means of establishing general theorems, for the asymptotic behavior of its solutions. Namely, we state new necessary and sufficient conditions for local asymptotic stability of these equations. In addition, we study the periodic solution with period two and three. Our results essentially extend and improve the earlier ones
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