A non-local in time telegraph equation. (April 2020)

• Record Type: Journal Article
• Authors: Pozo, Juan C.; Vergara, Vicente
• Is Part Of: Nonlinear analysis. Volume 193(2020)
• Publication Date: 2020-04
• Subjects: Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.01.001
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this work, we derive a non-local in time telegraph equation. Our model includes as particular cases the classical telegraph equation and the fractional in time telegraph equation among others. Further, we define the fundamental solution of the problem and we prove that it can be interpreted as a probability density function. Finally, using versions of the Karamata–Feller Tauberian theorem, we study the temporal behavior of the variance of the distribution process associated with the solution of the equation in large times as well as in short times.