Mathematics and Computer Science: Research Updates Vol. 7

Non-archimedean pseudo-differential operators have gained popularity in recent years due to their utility in studying certain equations associated with new physical models in physical form. Main aim of this paper is to define non-archimedean pseudo-differential operator associted with fractional Fourier transform in this manuscript. In this manuscript, we discuss some classes of p-adic complete inner product spaces, B_ϕ, _k(Q_p), 0 ≤ k < ∞, connected to negative definite, radial and continuous functions ϕ : Q_p → C. In this article, we also introduce the non-archimedean pseudo-differential operator A_ϕ,k involving fractional Fourier transform connected to negative definite functions. We find the convolution Kernel Kk of these operators and the Green function related to fractional Fourier transform.