In this paper, by applying Mahgoub transform, we show that the \(n^{\rm th}\) order linear differential equation \[x^{(n)}(v)+\sum_{\kappa=0}^{n-1}a_\kappa x^{(\kappa)}(v)=\psi(v)\] has Hyers-Ulam stability, where \(a_\kappa\)'s are scalars and \(x\) is an \(n\) times continuously differentiable function of exponential order.

Abstract. We calculate the fibre integrals of the affine hypersurface in a torus in the form of their Mellin transforms. Especially, our method works efficiently for an affine hypersurface defined by a so called “simpliciable” polynomial. The relations between poles of Mellin transforms of fibre integrals, the mixed Hodge structure of the cohomology of the hypersruface, the hypergeometric diffe...

We use the well-known observation that solutions of Jacobi's differential equation can be represented via non-oscillatory phase and amplitude functions to develop a fast algorithm for computing multi-dimensional Jacobi polynomial transforms. More explicitly, it follows from this matrix corresponding discrete transform is Hadamard product numerically low-rank Fourier (DFT) matrix. The applicatio...

The complementary differential operator is devised to decouple two coupled partial differential equations with variable coefficients. This complementary operator transforms two coupled partial differential equations into a pair of uncoupled equations either of (i) fourth order, (ii) third order, or (iii) second order. The conditions for the existence of linearly dependent solutions for two coup...

In this study, we introduce a novel generalization of triple integral transforms, which is called general transform. We present the definition new approach and prove main properties related to existence, uniqueness, shifting, scaling, inverse. Moreover, relations between transform other transforms are presented, results partial derivatives convolution theorem established. apply solve some appli...

In this paper we aim to construct an abstract model of a differential operator with fractional integro-differential composition in final terms, where modeling is understood as interpretation concrete operators terms the infinitesimal generator corresponding semigroup. We study such Kipriyanov operator, Riesz potential, difference operator. Along this, consider transforms m-accretive generalizat...