ANALYTICAL AND NUMERICAL STUDY OF A NONLINEAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATION WITH THE CAPUTO-FABRIZIO FRACTIONAL DERIVATIVE

被引：0

作者：

Bekkouche, Mohammed Moumen ^{[1
]}

Ahmed, Abdelaziz Azeb ^{[1
]}

Yazid, Fares ^{[2
]}

Djeradi, Fatima Siham ^{[2
]}

机构：

[1] El Oued Univ, Fac Exact Sci, Dept Math, El Oued 39000, Algeria

[2] Amar Teledji Univ Laghouat, Lab Pure & Appl Math, Laghouat 03000, Algeria

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2023年 / 16卷 / 08期

关键词：

Nonlinear integro-differential equation; Caputo-Fabrizio fractional de-rivative; convergence; existence and uniqueness of solution; nonsingular kernel;

D O I：

10.3934/dcdss.2023040

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we interest concerns an integro-differential equation of Volterra when the derivative of the solution appears under the sign of integration in a non-linear way. The derivation is the Caputo-Fabrizio Fractional Derivative (CF-FD), which increases the interest of this study. we built Lipchitz conditions to obtain the existence and uniqueness of the solution in a Banach space specific to the derivative of Caputo. The analytical study is followed by a complete numerical study.

引用

页码：2177 / 2193

页数：17

共 28 条

[1] Nonlinear fractional differential inclusions with non-singular Mittag-Leffler kernel [J].

Abbas, Mohamed I. ;

Ragusa, Maria Alessandra .

AIMS MATHEMATICS, 2022, 7 (11) :20328-20340

[2] Numerical solution of the system of nonlinear Volterra integro-differential equations with nonlinear differential part by the operational Tau method and error estimation [J].

Abbasbandy, S. ;

Taati, A. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 231 (01) :106-113

[3]

Atkinson K., 2001, THEORETICAL NUMERICA

[4]

Awawdeh F, 2011, ANN UNIV CRAIOVA-MAT, V38, P1

[5] 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-&

[6]

Caputo M, 2016, Progress in Fractional Differentiation and Applications, V2, P1, DOI [10.18576/pfda/020101, DOI 10.12785/PFDA/010201]

[7] Numerical solution of nonlinear Volterra-Fredholm integro-differential equations [J].

Darania, P. ;

Ivaz, K. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (09) :2197-2209

[8] Existence Results for a Nonlinear Fractional Differential Inclusion [J].

Djourdem, Habib .

FILOMAT, 2021, 35 (03) :927-939

[9] Analytical and numerical study for an integro-differential nonlinear volterra equation with weakly singular kernel [J].

Ghiat, Mourad ;

Guebbai, Hamza .

COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37 (04) :4661-4674

[10] Analytical and numerical study for an integro-differential nonlinear Volterra equation [J].

Guebbai, H. ;

Aissaoui, M. Z. ;

Debbar, I. ;

Khalla, B. .

APPLIED MATHEMATICS AND COMPUTATION, 2014, 229 :367-373

← 1 2 3 →