On the separation of solutions to fractional differential equations of order α ∈ (1,2)

Given the Caputo-type fractional differential equation Dαy(t)=f(t,y(t)) with α∈(1,2), we consider two distinct solutions y1,y2∈C[0,T] to this equation subject to different sets of initial conditions. In this framework, we discuss nontrivial upper and lower bounds for the difference |y1(t)−y2(t)| for...

Full description

Saved in:
Bibliographic Details
Published inApplied numerical mathematics Vol. 203; pp. 84 - 96
Main Authors Chaudhary, Renu, Diethelm, Kai, Hashemishahraki, Safoura
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.09.2024
Subjects
Caputo derivative
Fractional differential equation
Initial condition
Separation of solutions
Zeros of two-parameter Mittag-Leffler functions
Fractional differential equation
Separation of solutions
Initial condition
Zeros of two-parameter Mittag-Leffler functions
Caputo derivative
Online AccessGet full text
ISSN0168-9274
DOI10.1016/j.apnum.2024.05.020

Cover

More Information
Summary:Given the Caputo-type fractional differential equation Dαy(t)=f(t,y(t)) with α∈(1,2), we consider two distinct solutions y1,y2∈C[0,T] to this equation subject to different sets of initial conditions. In this framework, we discuss nontrivial upper and lower bounds for the difference |y1(t)−y2(t)| for t∈[0,T]. The main emphasis is on describing how such bounds are related to the differences of the associated initial values.
ISSN:0168-9274
DOI:10.1016/j.apnum.2024.05.020