Solving nonlinear matrix and Riesz-Caputo fractional differential equations via fixed point theory in partial metric spaces

被引：0

作者：

Nashine, Hemant Kumar ^{[1
,2
]}

Jain, Reena ^{[1
]}

Kadelburg, Zoran ^{[3
]}

机构：

[1] VIT Bhopal Univ, Sch Adv Sci & Languages, Math Div, Sehore 466114, Madhya Pradesh, India

[2] Univ Johannesburg, Dept Math & Appl Math, Kingsway Campus, ZA-2006 Auckland Pk, South Africa

[3] Univ Belgrade, Fac Math, Studentski Trg 16, Belgrade 11000, Serbia

来源：

FILOMAT | 2024年 / 38卷 / 02期

关键词：

Relational metric space; partial metric space; fixed point; positive definite matrix; nonlinear matrix equation; Riesz-Caputo fractional differential equation; PARTIALLY ORDERED SETS; MAPPINGS;

D O I：

10.2298/FIL2402645N

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A modified implicit relation and omega-implicit contractive condition are introduced in the setting of relational partial metric spaces and some related fixed point results are derived. Two suitable examples are provided. As an application, sufficient conditions are derived for the existence of a unique positive definite solution of the non-linear matrix equation X = B + Sigma(k)(i=1) A(i)*T(X)A(i). An example is given, using matrices that are randomly generated, as well as convergence and error analysis and average CPU time analysis. Solving fractional differential equations of Riesz-Caputo type with anti-periodic boundary conditions is also discussed, followed by two illustrations.

引用

页码：645 / 660

页数：16

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