Summability of formal solutions for a family of generalized moment integro-differential equations

TL;DR

This paper establishes generalized summability conditions for formal solutions of linear moment integro-differential equations with variable coefficients, including fractional cases, based on the behavior of moment derivatives.

Contribution

It introduces new summability results for formal solutions of moment integro-differential equations, extending to fractional and practical high-interest problems.

Findings

Summability results apply to a wide class of integro-differential equations.

Refined results provide more accurate summability conditions.

Applicable to fractional integro-differential equations in practice.

Abstract

Generalized summability results are obtained regarding formal solutions of certain families of linear moment integro-differential equations with time variable coefficients. The main result leans on the knowledge of the behavior of the moment derivatives of the elements involved in the problem. A refinement of the main result is also provided giving rise to more accurate results which remain valid in wide families of problems of high interest in practice, such as fractional integro-differential equations.