On a method for constructing a solution of integro-differential equations of fractional order

被引：5
作者：
Turmetov, Batirkhan Kh [1 ]
机构：
[1] Akhmet Yasawi Int Kazakh Turkish Univ, 29 B Sattarkhanov Ave, Turkestan 161200, Kazakhstan
来源：
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS | 2018年 / 25期
关键词：
integro-differential equation of Volterra type; Riemann-Liouville fractional integrals and derivatives; generalized Mittag-Leffler function; method normalized systems of functions; DIFFERENTIAL-EQUATIONS; UNIQUENESS; EXISTENCE;
D O I：
10.14232/ejqtde.2018.1.25
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we propose a new method for constructing a solution of the integro-differential equations of Volterra type. The particular solutions of the homogeneous and of the inhomogeneous equation will be constructed and the Cauchy type problems will be investigated. Note that this method is based on construction of normalized systems functions with respect to the differential operator's fractional order.
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页码：1 / 14
页数：14
相关论文
共 17 条
[1]   Solution of a fractional differintegral equation [J].
AlSaqabi, BN ;
Tuan, VK .
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 1996, 4 (04) :321-326
[2]   OPERATOR METHOD FOR CONSTRUCTION OF SOLUTIONS OF LINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS [J].
Ashurov, Ravshan ;
Cabada, Alberto ;
Turmetov, Batirkhan .
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2016, 19 (01) :229-252
[3]  
Becker LC, 2015, ELECTRON J QUAL THEO, P1
[4]  
Erugin N. P., 1970, KNIGA CHTENIYA OBSHC
[5]   Existence and uniqueness for a problem involving Hilfer fractional derivative [J].
Furati, K. M. ;
Kassim, M. D. ;
Tatar, N. E- .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 64 (06) :1616-1626
[6]   On the generalized Mittag-Leffler type functions [J].
Gorenflo, R ;
Kilbas, AA ;
Rogosin, SV .
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 1998, 7 (3-4) :215-224
[7]  
Graef JR, 2013, ELECTRON J QUAL THEO, P1
[8]   Sensitivity of a Fractional Integrodifferential Cauchy Problem of Volterra Type [J].
Idczak, Dariusz ;
Skowron, Andrzej ;
Walczak, Stanislaw .
ABSTRACT AND APPLIED ANALYSIS, 2013,
[9]   On fractional Cauchy-type problems containing Hilfer's derivative [J].
Kamocki, Rafal ;
Obczynski, Cezary .
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2016, (50) :1-12
[10]   ON SOME SPECIAL POLYNOMIALS AND FUNCTIONS [J].
Karachik, V. V. .
SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2013, 10 :205-226
12