Generalized fractional differential equations for past dynamic-Reference-Cited by-同舟云学术

Generalized fractional differential equations for past dynamic

Published:2022 Issue:8 Volume:7 Page:14394-14418
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Baleanu Dumitru¹²³,Shiri Babak⁴

Affiliation:

1. Cankaya University, Department of Mathematics, 06530 Balgat, Ankara, Turkey

2. Institute of Space Sciences, Magurele-Bucharest, Romania

3. Department of Medical Research, China Medical University Hospital, China Medical, University, Taichung, Taiwan

4. Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, China

Abstract

<abstract><p>Well-posedness of the terminal value problem for nonlinear systems of generalized fractional differential equations is studied. The generalized fractional operator is formulated with a classical operator and a related weighted space. The terminal value problem is transformed into weakly singular Fredholm and Volterra integral equations with delay. A lower bound for the well-posedness of the corresponding problem is introduced. A collocation method covering all problems with generalized derivatives is introduced and analyzed. Illustrative examples for validation and application of the proposed methods are supported. The effects of various fractional derivatives on the solution, well-posedness, and fitting error are studied. An application for estimating the population of diabetes cases in the past is introduced.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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