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

A. Benaissa Cherif a,c∗ and F. Z. Ladrani b,c

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

Authors :

A. Benaissa Cherif ^a,c∗and F. Z. Ladrani^b,c

Author Address :

^aDepartment of Mathematics, University of Ain Temouchent, BP 284, 46000 Ain Temouchent, Algeria.
^bDepartment of Biomathematics, Higher normal school of Oran, BP 1523, 31000 Oran, Algeria.
^cLaboratory of Mathematics, Sidi Bel Abbes University, 22000 Sidi Bel Abbes, Algeria.

*Corresponding author.

Abstract :

In this paper, we will establish asymptotic behavior of solutions for the fractional order nonlinear dynamic equation on time scales%
egin{equation*}
left( pleft( t ight) _{t_{0}}^{mathbb{T}}mathcal{D}_{t}^{alpha
}xleft( t ight) ight) ^{Delta }+fleft( t,x^{sigma }left( t ight)
ight) =0 ext{,qquad for all }tin left[ t_{0},+infty ight) _{mathbb{%
T}},
end{equation*}%
with $alpha in left[ 0,1 ight) $, where $_{t_{0}}^{mathbb{T}}mathcal{D}% _{t}^{alpha }x$ 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.

DOI :

Article Info :

Received : April 22, 2017; Accepted : May 31, 2017.