Van der Corput lemmas for Mittag-Leffler functions. II. ?–directions

The paper is devoted to study analogues of the van der Corput lemmas involving Mittag-Leffler functions. generalisation that we replace exponential function with Mittag-Leffler-type function, oscillatory integrals appearing in analysis time-fractional partial differential equations. More specifically, integral form I?,?(?)=?RE?,?(i???(x))?(x)dx, for range 00. This extends variety estimates obtained first part, where functions E?,?(i??(x)) have been studied. Several generalisations are proved. As an application above results, generalised Riemann-Lebesgue lemma, Cauchy problem Klein-Gordon and Schrödinger equations considered.