Abstract
Here, we propose a general framework covering a wide variety of fractional operators. We consider integral and differential operators and their role in tempered fractional calculus and study their analytic properties. We investigate tempered fractional integral operators acting on subspaces of L1[a,b], such as Orlicz or Hölder spaces. We prove that in this case, they map Orlicz spaces into (generalized) Hölder spaces. In particular, they map Hölder spaces into the same class of spaces. The obtained results are a generalization of classical results for the Riemann–Liouville fractional operator and constitute the basis for the use of generalized operators in the study of differential and integral equations. However, we will show the non-equivalence differential and integral problems in the spaces under consideration.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.