On the Caputo-Hadamard fractional IVP with variable order using the upper-lower solutions technique

被引：6

作者：

Bouazza, Zoubida ^{[1
]}

Souhila, Sabit ^{[2
]}

Etemad, Sina ^{[3
]}

Souid, Mohammed Said ^{[4
]}

Akguel, Ali ^{[5
,6
]}

Rezapour, Shahram ^{[3
,7
]}

De la Sen, Manuel ^{[8
]}

机构：

[1] Univ Tiaret, Dept Informat, Tiaret, Algeria

[2] Univ Tiaret, Dept Math, Lab Mat & Struct, Tiaret, Algeria

[3] Azarbaijan Shahid Madani Univ, Dept Math, Tabriz, Iran

[4] Univ Tiaret, Dept Econ Sci, Tiaret, Algeria

[5] Siirt Univ, Art & Sci Fac, Dept Math, TR-56100 Siirt, Turkiye

[6] Near East Univ, Math Res Ctr, Dept Math, Mersin 10, TR-99138 Nicosia, North Cyprus, Cyprus

[7] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung, Taiwan

[8] Univ Basque Country, Fac Sci & Technol, Inst Res & Dev Proc, Dept Elect & Elect, Leioa 48940, Bizkaia, Spain

来源：

AIMS MATHEMATICS | 2023年 / 8卷 / 03期

关键词：

fractional variable order; Caputo-Hadamard fractional derivative; upper-lower solutions; existence results; DIFFERENTIAL-EQUATIONS; MODEL;

D O I：

10.3934/math.2023276

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper studies the existence of solutions for Caputo-Hadamard fractional nonlinear differential equations of variable order (CHFDEVO). We obtain some needed conditions for this purpose by providing an auxiliary constant order system of the given CHFDEVO. In other words, with the help of piece-wise constant order functions on some continuous subintervals of a partition, we convert the main variable order initial value problem (IVP) to a constant order IVP of the Caputo-Hadamard differential equations. By calculating and obtaining equivalent solutions in the form of a Hadamard integral equation, our results are established with the help of the upper-lower-solutions method. Finally, a numerical example is presented to express the validity of our results.

引用

页码：5484 / 5501

页数：18

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[1] Existence of positive solutions for weighted fractional order differential equations [J].