Uncertain Fractional Evolution Equations with Non-Lipschitz Conditions Using the Condensing Mapping Approach

This paper studies the solvability of Cauchy problems for fractional evolution equations with uncertainty. By using a new approach based on the concept of non-compactness measure and the principle of condensing mappings in the spaces without linearity, we prove the existence of C 0 −solutions withou...

Full description

Saved in:
Bibliographic Details
Published inActa mathematica vietnamica Vol. 46; no. 4; pp. 795 - 820
Main Author Son, Nguyen Thi Kim
Format Journal Article
LanguageEnglish
Published Singapore Springer Singapore 01.12.2021
Springer Nature B.V
Subjects
Continuity (mathematics)
Evolution
Mathematical analysis
Mathematics
Mathematics and Statistics
Uncertainty
47H08
37L05
Fractional evolution equations
Condensing mappings
Non-Lipschitz conditions
Online AccessGet full text

Cover

More Information
Summary:This paper studies the solvability of Cauchy problems for fractional evolution equations with uncertainty. By using a new approach based on the concept of non-compactness measure and the principle of condensing mappings in the spaces without linearity, we prove the existence of C 0 −solutions without assuming the Lipschitz continuity of the function on the right-hand side. The present results extend previous results when external forces are always required to satisfy some kinds of generalized Lipschitz conditions. Moreover, the principle of condensing mappings for fuzzy-valued functions or set-valued functions found as an application of noncompactness measure is a useful result when studying dynamical systems containing uncertainties.
ISSN:0251-4184
2315-4144
DOI:10.1007/s40306-020-00405-y