Solutions of Riesz-Caputo fractional derivative problems involving anti-periodic boundary conditions

被引:1
|
作者
Edward, Jenisha Linnet [1 ]
Chanda, Ankush [1 ]
Nashine, Hemant Kumar [2 ,3 ]
机构
[1] Vellore Inst Technol, Sch Adv Sci, Dept Math, Vellore, India
[2] VIT Bhopal Univ, Sch Adv Sci & Languages, Math Div, Sehore 466114, Madhya Pradesh, India
[3] Univ Johannesburg, Dept Math & Appl Math, Kingsway Campus, ZA-2006 Auckland Pk, South Africa
关键词
Fixed point theorems; fractional differential equations; Riesz-Caputo derivative; anti-periodic boundary conditions; DIFFERENTIAL-EQUATIONS; SPACE;
D O I
10.2298/FIL2417177E
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This article deals with the investigation concerning the existence and uniqueness of anti-periodic boundary value solutions for a kind of Riesz-Caputo fractional differential equations. The equation is as follows (RC) (0) D (zeta) (l) Pi(tau) + T tau, Pi(tau), (RC) D-0(l)eta Pi ( tau )= 0 , tau is an element of J := [0, l ] , a(1) Pi (0) + b(1) Pi ( l ) = 0, a(2) Pi ' (0) + b2 Pi ' ( l ) = 0, a(3)Pi '' (0) + b(3) Pi '' ( l ) = 0, where 2 < zeta <= 3 and, 1 < eta <= 2, (RC) (0) D kappa l is the Riesz-Caputo fractional derivative of order kappa is an element of {zeta, eta}, T : J x R x R -> R is a continuous function and a i , b(i) are non-negative constants with a(i) > b(i) , i = 1, 2, 3. Uniqueness is demonstrated using Banach contraction principle, and existence is demonstrated employing the fixed point theorems of Schaefer and Krasnoselskii. Our results are supported by suitable numerical illustrations.
引用
收藏
页码:6177 / 6192
页数:16
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