On well-posedness of vector-valued fractional differential-difference equations

Abadias, L. (Universidad de Zaragoza) ; Lizama, C. ; Miana, P.J. (Universidad de Zaragoza) ; Velasco, M.P.

Resumen: We develop an operator-theoretical method for the analysis on well posedness of partial differential-difference equations that can be modeled in the form (*) {Delta(alpha) u(n) = Au(n + 2) + f(n, u(n)), n is an element of N-0, 1 < alpha <= 2; u(0) = u(0); u(1) = u(1); where A is a closed linear operator defined on a Banach space X. Our ideas are inspired on the Poisson distribution as a tool to sampling fractional differential operators into fractional differences. Using our abstract approach, we are able to show existence and uniqueness of solutions for the problem (*) on a distinguished class of weighted Lebesgue spaces of sequences, under mild conditions on sequences of strongly continuous families of bounded operators generated by A, and natural restrictions on the nonlinearity f. Finally we present some original examples to illustrate our results.

Idioma: Inglés

DOI: 10.3934/dcds.2019112

Año: 2019

Publicado en: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 39, 5 (2019), 2679-2708
ISSN: 1078-0947

Factor impacto JCR: 1.338 (2019)

Categ. JCR: MATHEMATICS rank: 64 / 324 = 0.198 (2019) - Q1 - T1
Categ. JCR: MATHEMATICS, APPLIED rank: 104 / 260 = 0.4 (2019) - Q2 - T2

Factor impacto SCIMAGO: 1.362 - Analysis (Q1) - Discrete Mathematics and Combinatorics (Q1) - Applied Mathematics (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E64
Financiación: info:eu-repo/grantAgreement/ES/MCYTS/ESP2016-79135-R
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2016-77710-P

Tipo y forma: Artículo (PrePrint)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)