An Efficient Approach for Solving Differential Equations in the Frame of a New Fractional Derivative Operator

被引：10

作者：

Attia, Nourhane ^{[1
]}

Akgul, Ali ^{[2
,3
,4
]}

Seba, Djamila ^{[5
]}

Nour, Abdelkader ^{[5
]}

De la Sen, Manuel ^{[6
]}

Bayram, Mustafa ^{[7
]}

机构：

[1] Ecole Natl Super Sci Mer & Amenagement Littoral, Campus Univ Dely Ibrahim,BP 19, Algiers 16320, Algeria

[2] Lebanese Amer Univ, Dept Comp Sci & Math, Beirut 11022801, Lebanon

[3] Siirt Univ, Art & Sci Fac, Dept Math, TR-56100 Siirt, Turkiye

[4] Near East Univ, Math Res Ctr, Dept Math, Near East Blvd, TR-99138 Nicosia, Turkiye

[5] Univ Mhamed Bougara Boumerdes, Fac Engineers Sci, Dynam Engines & Vibroacoust Lab, Boumerdes 35000, Algeria

[6] Univ Basque Country, Fac Sci & Technol, Inst Res & Dev Proc, Dept Elect & Elect, Leioa 48940, Bizkaia, Spain

[7] Biruni Univ, Dept Comp Engn, TR-34010 Istanbul, Turkiye

来源：

SYMMETRY-BASEL | 2023年 / 15卷 / 01期

关键词：

fractional differential equations; proportional-Caputo hybrid operator; constant proportional-Caputo operator; reproducing kernel Hilbert space method; ORDER;

D O I：

10.3390/sym15010144

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Recently, a new fractional derivative operator has been introduced so that it presents the combination of the Riemann-Liouville integral and Caputo derivative. This paper aims to enhance the reproducing kernel Hilbert space method (RKHSM, for short) for solving certain fractional differential equations involving this new derivative. This is the first time that the application of the RKHSM is employed for solving some differential equations with the new operator. We illustrate the convergence analysis of the applicability and reliability of the suggested approaches. The results confirm that the RKHSM finds the true solution. Additionally, these numerical results indicate the effectiveness of the proposed method.

引用

页数：25

共 28 条

[1] On conformable fractional calculus [J].

Abdeljawad, Thabet .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 279 :57-66

[2] A novel method for a fractional derivative with non-local and non-singular kernel [J].

Akgul, Ali .

CHAOS SOLITONS & FRACTALS, 2018, 114 :478-482

[3] Fractional View Analysis of Kuramoto-Sivashinsky Equations with Non-Singular Kernel Operators [J].

Alshehry, Azzh Saad ;

Imran, Muhammad ;

Khan, Adnan ;

Shah, Rasool ;

Weera, Wajaree .

SYMMETRY-BASEL, 2022, 14 (07)

[4]

Anderson D.R., 2015, Advances in Dynamical Systems and Applications, V10, P109

[5] New properties of conformable derivative [J].

Atangana, Abdon ;

Baleanu, Dumitru ;

Alsaedi, Ahmed .

OPEN MATHEMATICS, 2015, 13 :889-898

[6] RKM for solving Bratu-type differential equations of fractional order [J].

Babolian, Esmail ;

Javadi, Shahnam ;

Moradi, Eslam .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2016, 39 (06) :1548-1557

[7]

Baleanu D., 2017, FRACTIONAL CALCULUS, DOI DOI 10.1142/8180

[8] On a Fractional Operator Combining Proportional and Classical Differintegrals [J].

Baleanu, Dumitru ;

Fernandez, Arran ;

Akgul, Ali .

MATHEMATICS, 2020, 8 (03)

[9] Symmetric and Anti-Symmetric Solitons of the Fractional Second- and Third-Order Nonlinear Schrodinger Equation [J].

Cao, Qi-Hao ;

Dai, Chao-Qing .

CHINESE PHYSICS LETTERS, 2021, 38 (09)

[10] Lie Symmetry Analysis of the Time Fractional Generalized KdV Equations with Variable Coefficients [J].

Chen, Cheng ;

Jiang, Yao-Lin ;

Wang, Xiao-Tian .

SYMMETRY-BASEL, 2019, 11 (10)

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