Density solutions to a class of integro-differential equations

作者：Jedidi Wissem; Simon Thomas^*; Wang Mm

来源：Journal of Mathematical Analysis and Applications, 2018, 458(1): 134-152.

DOI：10.1016/j.jmaa.2017.08.043

• Beta distribution
• Double Gamma function
• Generalized Gamma convolution
• Integro-differential equation
• Riemann-Liouville operator
• Stable distribution

We consider the integro-differential equation I(0+)(alpha)f = x(m)f on the half-line. We show that there exists a density solution, which is then unique and can be expressed in terms of the Beta distribution, if and only if m > alpha. These density solutions extend the class of generalized one-sided stable distributions introduced in [29] and more recently investigated in [27]. We study various analytical aspects of these densities, and we solve the open problems about infinite divisibility formulated in [27].

• 出版日期2018-2-1