Work

The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces IV

Year: 2026

Type: article

Abstract: In this manuscript, we extend our previous work on the Riemann-Liouville fractional integral of order $$\alpha > 0$$ α > 0 in $$L^p(t_0,t_1;X)$$ L p ( t 0 , t 1 ; X ) . In particular, we establish its boundedness for the case $$\alpha > 1/p$$ α > 1 / p , with $$1< p < \infty $$ 1 < p < ∞ , as well as the case $$\alpha >0$$ α > 0 with $$p = \infty $$ p = ∞ . Moreover, we present a comprehensive summary of the results obtained so far.

Source: Fractional Calculus and Applied Analysis

DOI: 10.1007/s13540-026-00480-2

Authors: Paulo Mendes Carvalho Neto, Renato Fehlberg Júnior

Institutions: Universidade Federal de Santa Catarina, Universidade Federal do Espírito Santo

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,590

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Fundação de Amparo à Pesquisa e Inovação do Espírito Santo