INVERSE PROBLEMS FOR DIFFUSION EQUATION WITH FRACTIONAL DZHERBASHIAN-NERSESIAN OPERATOR

被引：14

作者：

Ahmad, Anwar ^{[1
]}

Ali, Muhammad ^{[2
]}

Malik, Salman A. ^{[1
]}

机构：

[1] COMSATS Univ Islamabad, Dept Math, Pk Rd, Islamabad 45550, Pakistan

[2] Natl Univ Comp & Emerging Sci, Dept Sci & Humanities, Islamabad, Pakistan

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2021年 / 24卷 / 06期

关键词：

fractional Dzherbashian-Nersesian operator; inverse problems; fractional differential equations; Mittag-Leffler function; FAMILY;

D O I：

10.1515/fca-2021-0082

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Fractional Dzherbashian-Nersesian operator is considered and three fa-mous fractional order derivatives named after Riemann-Liouville, Caputo and Hilfer are shown to be special cases of the earlier one. The expres-sion for Laplace transform of fractional Dzherbashian-Nersesian operator is constructed. Inverse problems of recovering space dependent and time de-pendent source terms of a time fractional diffusion equation with involution and involving fractional Dzherbashian-Nersesian operator are considered. The results on existence and uniqueness for the solutions of inverse prob-lems are established. The results obtained here generalize several known results.

引用

页码：1899 / 1918

页数：20

共 25 条

[1] BOUNDED SOLUTIONS FOR DIFFERENTIAL-EQUATIONS WITH REFLECTION OF THE ARGUMENT [J].

AFTABIZADEH, AR ;

YONG, KH ;

WIENER, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1988, 135 (01) :31-37

[2] INITIAL-BOUNDARY VALUE PROBLEMS FOR A TIME-FRACTIONAL DIFFERENTIAL EQUATION WITH INVOLUTION PERTURBATION [J].

Al-Salti, Nasser ;

Kerbal, Sebti ;

Kirane, Mokhtar .

MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2019, 14 (03)

[3] INVERSE PROBLEM FOR A MULTI-TERM FRACTIONAL DIFFERENTIAL EQUATION [J].

Ali, Muhammad ;

Aziz, Sara ;

Malik, Salman A. .

FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2020, 23 (03) :799-821

[4] INVERSE SOURCE PROBLEM FOR A SPACE-TIME FRACTIONAL DIFFUSION EQUATION [J].

Ali, Muhammad ;

Aziz, Sara ;

Malik, Salman A. .

FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2018, 21 (03) :844-863

[5] Inverse problem for a space-time fractional diffusion equation: Application of fractional Sturm-Liouville operator [J].

Ali, Muhammad ;

Aziz, Sara ;

Malik, Salman A. .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (07) :2733-2747

[6] An inverse problem for a family of two parameters time fractional diffusion equations with nonlocal boundary conditions [J].

Ali, Muhammad ;

Malik, Salman A. .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (18) :7737-7748

[7] An inverse problem for a family of time fractional diffusion equations [J].

Ali, Muhammad ;

Malik, Salman A. .

INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 2017, 25 (09) :1299-1322

[8] Analogs of classical boundary value problems for a second-order differential equation with deviating argument [J].

Andreev, AA .

DIFFERENTIAL EQUATIONS, 2004, 40 (08) :1192-1194

[9]

Aziz S., 2016, Electronic Journal of Differential Equations, V2016, P1

[10] LINEAR MODELS OF DISSIPATION WHOSE Q IS ALMOST FREQUENCY INDEPENDENT-2 [J].

CAPUTO, M .

GEOPHYSICAL JOURNAL OF THE ROYAL ASTRONOMICAL SOCIETY, 1967, 13 (05) :529-&

← 1 2 3 →