"Asymptotic Behavior of Solutions of Higher Order Fractional Differenti" by John R. Graef, Said R. Grace et al.

Progress in Fractional Differentiation & Applications

Article Title

Asymptotic Behavior of Solutions of Higher Order Fractional Differential Equations with a Caputo-Type Hadamard Derivative

Authors

John R. Graef, Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USAFollow
Said R. Grace
Ercan Tunc ̧

Author Country (or Countries)

USA

Abstract

The present paper investigates the behavior of nonoscillatory solutions of the higher order fractional differential equation C,HDary(t)=e(t)+f(t,x(t)), a>1, where C,HDar is a Caputo-type Hadamard derivative. The authors address the two cases y(t) = x(k)(t) with k a positive integer, and y(t) = 􏰀c(t)(x′(t))μ􏰁′ with μ ≥ 1 being the ratio of odd positive integers. Here, r = n+α −1, α ∈ (0,1), and n ∈ Z+.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/060101

Recommended Citation

R. Graef, John; R. Grace, Said; and Tunc ̧, Ercan (2020) "Asymptotic Behavior of Solutions of Higher Order Fractional Differential Equations with a Caputo-Type Hadamard Derivative," Progress in Fractional Differentiation & Applications: Vol. 6: Iss. 1, Article 1.
DOI: http://dx.doi.org/10.18576/pfda/060101
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol6/iss1/1

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