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Concept and application of interval-valued fractional conformable calculus.
- Source :
- Alexandria Engineering Journal; Dec2022, Vol. 61 Issue 12, p11959-11977, 19p
- Publication Year :
- 2022
-
Abstract
- This paper introduces a new concept of Caputo type interval-valued fractional conformable calculus. Based on this, some theorems and properties related to fractional conformable calculus are presented. As an application, this paper attempts to investigate an initial value problem of functional integro-differential equations with Caputo type interval-valued fractional conformable derivatives. We not only prove the existence of at least one solution, the extremal solutions and the unique solution of the above problem, but also establish some monotone iterative sequences converging to the extremal solutions. More meaningful and important, some comparison principles and generalized Gronwall inequality related to the proposed problem are also proved. Two examples are presented to illustrate the main results. We firmly believe that the concept of interval-valued fractional conformable calculus, new comparison principles and generalized Gronwall inequality introduced here can be conveniently applied to qualitative analysis of a variety of new interval-valued fractional conformable biological models, economic models, etc., which will better describe and explain various complex phenomena derived from the real world. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 11100168
- Volume :
- 61
- Issue :
- 12
- Database :
- Supplemental Index
- Journal :
- Alexandria Engineering Journal
- Publication Type :
- Academic Journal
- Accession number :
- 160909941
- Full Text :
- https://doi.org/10.1016/j.aej.2022.06.005