An integro-differential equation, modeling dynamic fractional order viscoelasticity, with a Mittag-Leffler type convolution kernel is considered. A discontinuous Galerkin method, based on piecewise constant polynomials is formulated for temporal semidiscretization of the problem. Stability estimates of the discrete problem are proved, that are used to prove optimal order a priori error estimate...

A novel procedure to reduce by four the order of Euler–Lagrange equations associated to n-th order variational problems involving single variable integrals is presented. In preparation, a new formula for the commutator of two C∞symmetries is established. The method is based on a pair of variational C∞-symmetries whose commutators satisfy a certain solvability condition. It allows one to recover...

New sufficient conditions of the existence and uniqueness of the solution of a boundary problem for an ordinary differential equation of n-th order with certain functional boundary conditions are constructed by the method of a priori estimates.

n this paper, we study the existence and uniqueness of an intuitionistic fuzzy solution for semi-linear integro-differential equations with non-local conditions using Banach fixed point theorem. Theorem on these problems nonlocal are presented under certain assumptions. Finally, example is established to illustrate effectiveness