GENERALIZED WEAKLY SINGULAR INTEGRAL INEQUALITIES WITH APPLICATIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS WITH RESPECT TO ANOTHER FUNCTION

被引：8

作者：

Boulares, Salah ^{[1
]}

Ben Makhlouf, Abdellatif ^{[2
]}

Khellaf, Hassane ^{[1
]}

机构：

[1] Univ Freres Mentouri, Constantine, Algeria

[2] Univ Sfax, Dept Math, Sfax, Tunisia

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2020年 / 50卷 / 06期

关键词：

fractional differential equations; integral inequalities;

D O I：

10.1216/rmj.2020.50.2001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We have established some new weakly singular integral inequalities, and our obtained inequalities generalize some recently obtained inequalities in the literature. Also, by involving a Caputo-type fractional derivative with respect to another function, we have obtained some applications to fractional differential equations.

引用

页码：2001 / 2010

页数：10

共 14 条

[1] FURTHER PROPERTIES OF OSLER'S GENERALIZED FRACTIONAL INTEGRALS AND DERIVATIVES WITH RESPECT TO ANOTHER FUNCTION
Almeida, Ricardo
[J]. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2019, 49 (08) : 2459 - 2493
[2] Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications
Almeida, Ricardo
Malinowska, Agnieszka B.
Monteiro, M. Teresa T.
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (01) : 336 - 352
[3] A Caputo fractional derivative of a function with respect to another function
Almeida, Ricardo
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2017, 44 : 460 - 481
[4] Caputo-Hadamard fractional differential equation with three-point boundary conditions in Banach spaces
Boutiara, Abdellatif
Guerbati, Kaddour
Benbachir, Maamar
[J]. AIMS MATHEMATICS, 2020, 5 (01): : 259 - 272
[5] Henry D., 1980, LECT NOTES MATH, V840, P1
[6] Kilbas AA, 2006, N HOLLAND MATH STUDI, V204
[7] Some new explicit bounds for weakly singular integral inequalities with applications to fractional differential and integral equations
Ma, Qing-Hua
Pecaric, Josip
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 341 (02) : 894 - 905
[8] Martynyuk A. A., 1977, MOTION STABILITY MET
[9] A new approach to an analysis of Henry type integral inequalities and their Bihari type versions
Medved, M
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 214 (02) : 349 - 366
[10] Integral inequalities and global solutions of semilinear evolution equations
Medved, M
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 267 (02) : 643 - 650

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