The Goursat’s problem for generalized (fractional) hyperbolic-type equation

We start by defining a novel bivariate Mittag-Leffler function represented by an infinite double series. Several key properties of this function are established, including differentiation formulas and an upper bound estimate. Subsequently, we consider Goursat’s problem for a fractional generalization of a hyperbolic-type equation. An explicit solution to this problem is constructed using the newly defined bivariate Mittag-Leffler function. The analytical characteristics derived for this function allow us to prove the unique solvability of the proposed problem.