Abstract
The paper is devoted to study multidimensional van der Corput-type estimates for the intergrals involving Mittag-Leffler functions. The generalisation is that we replace the exponential function with the Mittag-Leffler-type function, to study multidimensional oscillatory integrals appearing in the analysis of time-fractional evolution equations. More specifically, we study two types of integrals with functions E
α, β
(i λ ϕ(x)), x ∈ ℝ
N
and E
α, β
(i
α
λ ϕ(x)), x ∈ ℝ
N
for the various range of α and β. Several generalisations of the van der Corput-type estimates are proved. As an application of the above results, the Cauchy problem for the multidimensional time-fractional Klein-Gordon and time-fractional Schrödinger equations are considered.
Explicit Analytical Solution For A Kind Of Time-fractional Evolution Equations By Hes Homotopy Perturbation Methods
