NONNEGATIVITY OF SOLUTIONS OF NONLINEAR FRACTIONAL DIFFERENTIAL-ALGEBRAIC EQUATIONS

Xiaoli DING; Yaolin JIANG

doi:10.1016/S0252-9602(18)30781-1

Acta mathematica scientia, Series B >

2018 , Vol. 38 >Issue 3: 756 - 768

DOI: https://doi.org/10.1016/S0252-9602(18)30781-1

Articles

NONNEGATIVITY OF SOLUTIONS OF NONLINEAR FRACTIONAL DIFFERENTIAL-ALGEBRAIC EQUATIONS

Xiaoli DING ,
Yaolin JIANG

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1. Department of Mathematics, Xi'an Polytechnic University, Shaanxi 710048, China;
2. Department of Mathematics, Xi'an Jiaotong University, Shaanxi 710049, China

Received date: 2016-12-09

Revised date: 2017-03-11

Online published: 2018-06-25

Supported by

The work of the first author was supported by the Natural Science Foundation of China (NSFC) under grant 11501436 and Young Talent fund of University Association for Science and Technology in Shaanxi, China (20170701).

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Abstract

Nonlinear fractional differential-algebraic equations often arise in simulating integrated circuits with superconductors. How to obtain the nonnegative solutions of the equations is an important scientific problem. As far as we known, the nonnegativity of solutions of the nonlinear fractional differential-algebraic equations is still not studied. In this article, we investigate the nonnegativity of solutions of the equations. Firstly, we discuss the existence of nonnegative solutions of the equations, and then we show that the nonnegative solution can be approached by a monotone waveform relaxation sequence provided the initial iteration is chosen properly. The choice of initial iteration is critical and we give a method of finding it. Finally, we present an example to illustrate the efficiency of our method.

Key words： Fractional differential-algebraic equations; nonnegativity of solutions; waveform relaxation; monotone convergence

Cite this article

Xiaoli DING , Yaolin JIANG . NONNEGATIVITY OF SOLUTIONS OF NONLINEAR FRACTIONAL DIFFERENTIAL-ALGEBRAIC EQUATIONS[J]. Acta mathematica scientia, Series B, 2018 , 38(3) : 756 -768 . DOI: 10.1016/S0252-9602(18)30781-1

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