Lebesgue–Stieltjes combined $$\Diamond _\alpha $$-measure and integral on time scales

Fundamental solution matrix and Cauchy properties of quaternion combined impulsive matrix dynamic equation on time scales

“…In particular, for α = 1 the ♦ α diamond derivatives is ∆-derivatives, and for α = 0 the ♦ α diamond derivatives is ∇-derivatives. In 2020, Wang and Agarwal et.al established the combined measure theory on time scales and it was applied to study Lebesgue-Stieltjes combined ♦ α -measure and integral (see [16,42]). In [12], the non-eigenvalue form of Liouville's formula and αmatrix exponential solutions for combined matrix dynamic equations on time scales were obtained.…”