Novel non-hyper-singular [i.e., only strongly-singular] boundary-integral-equations for the gradients of the acoustic velocity potential, involving only O(r−2) singularities at the surface of a 3-D body, are derived, for solving problems of acoustics governed by the Helmholtz differential equation. The gradients of the fundamental solution to the Helmholtz differential equation for the velocity...

We obtain new numerical schemes for weakly singular integrals of convolution type called Caputo fractional order using Taylor and series expansions grouping terms in a novel manner. A expansion argument is utilized to provide fractional-order approximations functions with minimal regularity. The resulting allow the approximation Cγ[0,T], where 0<γ≤5. mild invertibility criterion provided implic...