ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH CAPUTO-TYPE HADAMARD DERIVATIVES

被引：17
|
作者：
Graef, John R. [1 ]
Grace, Said R. [2 ]
Tunc, Ercan [3 ]
机构：
[1] Univ Tennessee, Dept Math, Chattanooga, TN 37403 USA
[2] Cairo Univ, Fac Engn, Dept Engn Math, Giza 12613, Egypt
[3] Gaziosmanpasa Univ, Fac Arts & Sci, Dept Math, TR-60240 Tokat, Turkey
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2017年 / 20卷 / 01期
关键词：
asymptotic behavior; oscillation; Hadamard derivative; Caputo derivative; fractional differential equations; L-P-SOLUTIONS; INTEGRODIFFERENTIAL EQUATIONS; INTEGRATION;
D O I：
10.1515/fca-2017-0004
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the authors study the asymptotic behavior of solutions of higher order fractional differential equations with Caputo-type Hadamard derivatives of the form D-C, H(a)r x(t) = e(t) + f(t, x(t)), a > 1, where r = n+alpha-1, alpha is an element of (0, 1), and n is an element of Z(+). They also apply their technique to investigate the oscillatory and asymptotic behavior of solutions of the related integral equation x(t) = e(t) + integral(t)(a) (ln t/s)(r-1) k(t, s) f(s, x(s)) ds/s, a > 1, r is as above.
引用
收藏
页码：71 / 87
页数：17
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