Titchmarsh's theorem of Hankel transform

2019 ◽  
pp. 11-24
Author(s):  
Mohamed-Ahmed Boudref
Keyword(s):  
Number Theory ◽  
Data Analysis ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Lipschitz Condition ◽  
Analytic Number Theory ◽  
Hankel Transform ◽  
Partial Differential ◽  
Analytic Number ◽  
Bessel Transform

Hankel transform (or Fourier-Bessel transform) is a fundamental tool in many areas of mathematics and engineering, including analysis, partial differential equations, probability, analytic number theory, data analysis, etc. In this article, we prove an analog of Titchmarsh's theorem for the Hankel transform of functions satisfying the Hankel-Lipschitz condition.

scholarly journals Existence and Continuous Dependence for Fractional Partial Hyperbolic Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Qixiang Dong ◽  
Guangxian Wu ◽  
Lanping Zhu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Lipschitz Condition ◽  
Caputo Derivative ◽  
Continuous Dependence ◽  
Lipschitz Constant ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential ◽  
Continuous Dependence Results ◽  
Hyperbolic Differential Equations

This paper is concerned with a class of fractional hyperbolic partial differential equations with the Caputo derivative. Existence and continuous dependence results of solutions are obtained under the hypothesis of the Lipschitz condition without any restriction on the Lipschitz constant. Examples are discussed to illustrate the results.

scholarly journals Solving PDEs with Intrepid

2012 ◽  
Vol 20 (2) ◽  
pp. 151-180 ◽  
Author(s):  
P. Bochev ◽  
H.C. Edwards ◽  
R.C. Kirby ◽  
K. Peterson ◽  
D. Ridzal
Keyword(s):  
Data Analysis ◽  
Partial Differential Equations ◽  
Numerical Methods ◽  
Differential Equations ◽  
Software Design ◽  
General Context ◽  
Partial Differential ◽  
Mathematical Ideas ◽  
Wide Range ◽  
Local Cell

Intrepid is a Trilinos package for advanced discretizations of Partial Differential Equations (PDEs). The package provides a comprehensive set of tools for local, cell-based construction of a wide range of numerical methods for PDEs. This paper describes the mathematical ideas and software design principles incorporated in the package. We also provide representative examples showcasing the use of Intrepid both in the context of numerical PDEs and the more general context of data analysis.

Partial Differential Equations

2020 ◽  
Author(s):  
A. K. Nandakumaran ◽  
P. S. Datti
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential
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