2021
DOI: 10.1515/fca-2021-0061
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Summability of Formal Solutions for a Family of Generalized Moment Integro-Differential Equations

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 knowledg e 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 … Show more

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Cited by 8 publications
(4 citation statements)
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“…The last advances in the theory of the asymptotic behavior of solutions to moment functional equations have been obtained recently regarding the summability of certain families of moment integro-differential equations [12], and also Maillet-type theorems [11,24]. We mention the recent works by P. Remy in the study of partial differential equations [19] and integro-differential equations [20] of a similar nature as those considered in these works.…”
Section: Introductionmentioning
confidence: 82%
See 1 more Smart Citation
“…The last advances in the theory of the asymptotic behavior of solutions to moment functional equations have been obtained recently regarding the summability of certain families of moment integro-differential equations [12], and also Maillet-type theorems [11,24]. We mention the recent works by P. Remy in the study of partial differential equations [19] and integro-differential equations [20] of a similar nature as those considered in these works.…”
Section: Introductionmentioning
confidence: 82%
“…Lemma 11. In the situation of Theorem 2, one has that ∂ me,z u(z) is the M a -sum of ∂ me,z û(z) in G. In view of (12), this means that given u which admits û(z) = n≥0 u n z n as its asymptotic expansion at the origin in G, then lim z→0,z∈G…”
mentioning
confidence: 98%
“…Even more recently the notions of Gevrey estimates and summability have been applied to linear moment differential equations in [12,13,24] as well as their generalizations in the framework of strongly regular sequences in [7][8][9][10].…”
Section: Introductionmentioning
confidence: 99%
“…Recently, several summability results of the formal solutions to moment partial differential equations have been obtained by Michalik [24] and by Michalik et al [15], and also in the final section of the chapter [28], by Sanz. Also, some advances have been made on the study of moment integro-differential equations [17]. The knowlegdge of the growth of the coefficients of the (1) m y(z) = Ay(z), formal solutions to moment partial differential equations is also of great interest as a first step towards summability results [16,30], and also the Stokes phenomenon [26].…”
Section: Introductionmentioning
confidence: 99%