1 Overview We begin by recalling the Rolle’s Theorem.1 Using this result, we shall derive the Lagrange Form of the Taylor’s Remainder Theorem. Subsequently, we shall derive several mathematical inequalities as a corollary of this result. For example, 1. We shall use the Taylor’s Remainder Theorem to upper and lower bound exponential functions using polynomials. 2. We shall use the Taylor’ Remai...

In the three-dimensional open rectangular domain, problem of identification redefinition function for a partial differential equation with Gerasimov–Caputo-type fractional operator, degeneration, and integral form condition is considered in case 0<??1 order. A positive parameter present mixed derivatives. The solution this studied class regular functions. Fourier series method used, countabl...