By applying Slater's transformation formulas for the bilateral basic hypergeometric series ₂ψ₂, we derive three translation or connection formulas for the generalized Zwegers' μ-function ("continuous q-Hermite function") which was introduced by Shibukawa–Tsuchimi (SIGMA, 2023). From some Bailey's transformation formula of ₂ψ₂, we also give a formula for the expression of the generalized Zwegers' μ-function by a certain degenerate Very-Well-Poised bilateral basic hypergeometric series ₄ψ₈. As an application of this new expression formula for the generalized Zwegers' μ-function, we obtain some new q-expansions for elliptic functions and Ramanujan's mock theta functions.

In this study, we consider a fractional-order predator-prey model with a Holling-type functional response and stage structure for the prey. This study involved analyzing the existence and uniqueness of nonnegative solutions of the system. Conditions for the local asymptotic stability of the equilibria are established, and controllers are designed for the global asymptotic stability of the interior equilibrium. Furthermore, numerical simulations are performed to illustrate the results.

We prove that Sobolev norms of solutions to time-dependent Schrödinger equations for multi-particle systems interacting via time-dependent two body potentials are bounded in time if certain Sobolev norms of the potentials are small uniformly in time. The proof uses the scattering theory in the extended phase space which proves that all particles scatter freely in the remote past and far future.

In 1993, Gérard-Tahara introduced the Fuchs (Gérard-Tahara) type partial differential equation, and they determined the structure of holomorphic and singular solutions provided that the characteristic exponents satisfy some conditions. In this paper the author shows existences of holomorphic and singular solutions of difference-differential equations where the time variable derivative is replaced by q-difference operator.

In this paper, we find new regularity criteria on the magnetohydrodynamic (MHD) system in terms of partial components of the velocity field and the magnetic field in Lorentz space. Our aim is to refine and extend the criteria of the Lebesgue space in previous results to those of a larger Lorentz space.