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

作者：Graef John R^*; Grace Said R; Tunc Ercan

来源：Fractional Calculus and Applied Analysis, 2017, 20(1): 71-87.

DOI：10.1515/fca-2017-0004

• asymptotic behavior
• oscillation
• Hadamard derivative
• Caputo derivative
• fractional differential equations

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.

• 出版日期2017-2