Fractional Singular Differential Systems of Lane-Emden Type: Existence and Uniqueness of Solutions

被引：7

作者：

Gouari, Yazid ^{[1
]}

Dahmani, Zoubir ^{[2
]}

Farooq, Shan E. ^{[3
]}

Ahmad, Farooq ^{[4
,5
]}

机构：

[1] UMAB Univ Mostaganem, Fac SEI, Lab Pure & Appl Maths, Mostaganem 27000, Algeria

[2] Univ Mostaganem, UMAB, LPAM, Mostaganem 27000, Algeria

[3] Govt Coll Univ, Math Dept, Lahore 54000, Pakistan

[4] Univ Hail, Math Dept, Hail 55211, Saudi Arabia

[5] NANYANG Technol Univ, Sch Mech & Aerosp Engn, Singapore 637551, Singapore

来源：

AXIOMS | 2020年 / 9卷 / 03期

关键词：

Caputo derivative; lane emden system; existence of solution; singular differential equation; POSITIVE SOLUTIONS;

D O I：

10.3390/axioms9030095

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A coupled system of singular fractional differential equations involving Riemann-Liouville integral and Caputo derivative is considered in this paper. The question of existence and uniqueness of solutions is studied using Banach contraction principle. Furthermore, the question of existence of at least one solution is discussed. At the end, an illustrative example is given in details.

引用

页数：18

共 30 条

[1] Positive solutions for mixed problems of singular fractional differential equations [J].

Agarwal, Ravi P. ;

O'Regan, Donal ;

Stanek, Svatoslav .

MATHEMATISCHE NACHRICHTEN, 2012, 285 (01) :27-41

[2]

[Anonymous], 1907, Gaskugeln

[3]

[Anonymous], 1993, An Introduction to the Fractional Calculus and Fractional Differential Equations

[4] Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties [J].

Atangana, Abdon .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2018, 505 :688-706

[5] Decolonisation of fractional calculus rules: Breaking commutativity and associativity to capture more natural phenomena [J].

Atangana, Abdon ;

Gomez-Aguilar, J. F. .

EUROPEAN PHYSICAL JOURNAL PLUS, 2018, 133 (04)

[6]

Bahous Y., 2019, TURKISH J INEQ, V3, P35

[7] Existence and multiplicity of positive solutions for singular fractional boundary value problems [J].

Bai, Zhanbing ;

Sun, Weichen .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 63 (09) :1369-1381

[8]

Bekkouche Z., 2018, INT J OPEN PROBLEMS, V11, P15

[9] A class of nonlinear singular differential equations [J].

Benzidane, Abdelkader ;

Dahmani, Zoubir .

JOURNAL OF INTERDISCIPLINARY MATHEMATICS, 2019, 22 (06) :991-1007

[10] A numerical solution for a variable-order reaction-diffusion model by using fractional derivatives with non-local and non-singular kernel [J].

Coronel-Escamilla, A. ;

Gomez-Aguilar, J. F. ;

Torres, L. ;

Escobar-Jimenez, R. F. .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2018, 491 :406-424

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