Nonlinear multi-order fractional differential equations with periodic/anti-periodic boundary conditions

被引：21
|
作者：
Choudhary, Sangita [1 ]
Daftardar-Gejji, Varsha [1 ]
机构：
[1] Univ Pune, Dept Math, Pune 411007, Maharashtra, India
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2014年 / 17卷 / 02期
关键词：
fractional calculus; multi order Mittag-Leffler functions; fractional differential equations; periodic/ anti-periodic boundary conditions; DERIVATIVES;
D O I：
10.2478/s13540-014-0172-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the present manuscript we analyze non-linear multi-order fractional differential equation L(D)u(t) = f(t, u(t)), t is an element of [0, T], T > 0, where L(D) = lambda D-c(n)alpha n + lambda(n-1) D-c(alpha n-1) + . . . + lambda(1) D-c(alpha 1) + lambda(0) D-c(alpha 0), lambda(i) is an element of R (i = 0, 1, . . . , n), lambda(n) not equal 0, 0 <= alpha(0) < alpha(1) < . . . < alpha(n-1) < alpha(n) < 1, and D-c(alpha) denotes the Caputo fractional derivative of order alpha. We find the Greens functions for this equation corresponding to periodic/anti-periodic boundary conditions in terms of the two-parametric functions of Mittag-Leffler type. Further we prove existence and uniqueness theorems for these fractional boundary value problems.
引用
收藏
页码：333 / 347
页数：15
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