Volume 38, Issue 1

In this paper, we prove the analogous result of Fang [1] for transcendental E -valued meromorphic functions of finite order, which generalizes and improves the result of Wu [6].

We derive Mellin integral representations in terms of Macdonald functions for the squared absolute value s↦|Γ⁢(a+i⁢s)|2{s\mapsto|\Gamma(a+is)|^{2}} of the gamma function and its Fourier transform when a<0{a<0} is non-integer, generalizing known results in the case a>0{a>0}. This representation is based on a renormalization argument using modified Bessel functions of the second kind, and it applies to the representation of the solutions of a Fokker–Planck equation.

The initial value problem for an inhomogeneous nonlinear heat equation with a pure power nonlinearity is investigated. In the radial energy space, global and non-global well-posedness are discussed.

In this article, we study the Hyers–Ulam stability of the linear and nonlinear fractional differential equations with the Prabhakar derivative. By using the Laplace transform, we show that the introduced fractional differential equations with the Prabhakar fractional derivative is Hyers–Ulam stable. The results generalize the stability of ordinary and fractional differential equations in the Riemann–Liouville sense.

In this paper, we prove some new dynamic inequalities on time scales which as special cases contain several generalizations of integral and discrete inequalities due to Hardy, Copson, Leindler, Bennett, Pachpatte and Pečarić and Hanjš.