Asymptotic behavior of solution for a fractional Riemann-Liouville differential equations on time scales

A. Benaissa Cherif; F. Z. Ladrani

doi:10.26637/mjm503/011

Abstract

In this paper, we will establish asymptotic behavior of solutions for the fractional order nonlinear dynamic equation on time scales
$$
\left(p(t)_{t_0}^{\mathbb{T}} \mathcal{D}_t^\alpha x(t)\right)^{\Delta}+f\left(t, x^\sigma(t)\right)=0, \quad \text { for all } t \in\left[t_0,+\infty\right)_{\mathbb{T}}
$$
with $\alpha \in[0,1)$, where ${ }_{t_0}^{\mathrm{T}} \mathcal{D}_t^\alpha x$ is the Riemann-Liouville fractional derivative of order $\alpha$ of $x$ on time scales. We obtain some asymptotic behavior of solutions for the equation by developing a generalized Riccati substitution technique. Our results in this paper some sufficient conditions for asymptotic behavior of all solutions.

Keywords:

Oscillation, Dynamic equations, Time scale, Riccati technique, Fractional calculus

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

A. Benaissa Cherif Department of Mathematics, University of Ain Temouchent, BP 284, 46000 Ain Temouchent, Algeria. https://orcid.org/0000-0002-0995-3751
F. Z. Ladrani Department of Biomathematics, Higher normal school of Oran, BP 1523, 31000 Oran, Algeria. https://orcid.org/0000-0002-0995-3751

Pages: 561-568
Date Published: 01-07-2017
Vol. 5 No. 03 (2017): Malaya Journal of Matematik (MJM)

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