ANALYSIS AND NEW APPLICATIONS OF FRACTAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH POWER LAW KERNEL

被引：12

作者：

Akgul, Ali ^{[1
]}

机构：

[1] Siirt Univ, Art & Sci Fac, Dept Math, TR-56100 Siirt, Turkey

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2021年 / 14卷 / 10期

关键词：

power law kernel; reproducing kernel Hilbert space method; Malkus waterwheel model; numerical simulations;   Fractal fractional differential equations;

D O I：

10.3934/dcdss.2020423

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain the solutions of fractal fractional differential equations with the power law kernel by reproducing kernel Hilbert space method in this paper. We also apply the Laplace transform to get the exact solutions of the problems. We compare the exact solutions with the approximate solutions. We demonstrate our results by some tables and figures. We prove the efficiency of the proposed technique for fractal fractional differential equations.

引用

页码：3401 / 3417

页数：17

共 16 条

[1] Akgul A., 2019, DIFFER EQUAT DYN SYS
[2] REPRODUCING KERNEL FUNCTIONS FOR DIFFERENCE EQUATIONS
Akgul, Ali
Inc, Mustafa
Karatas, Esra
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2015, 8 (06): : 1055 - 1064
[3] [Anonymous], 1832, J ECOLE POLYTECHNIQU
[4] THEORY OF REPRODUCING KERNELS
ARONSZAJN, N
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1950, 68 (MAY) : 337 - 404
[5] Atangana A., DISCRET CONTIN DYN S
[6] Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system
Atangana, Abdon
[J]. CHAOS SOLITONS & FRACTALS, 2017, 102 : 396 - 406
[7] Reproducing Kernel Hilbert Spaces and fractal interpolation
Bouboulis, P.
Mavroforakis, M.
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (12) : 3425 - 3434
[8] Laplace homotopy analysis method for solving linear partial differential equations using a fractional derivative with and without kernel singular
Fabian Morales-Delgado, Victor
Francisco Gomez-Aguilar, Jose
Yepez-Martinez, Huitzilin
Baleanu, Dumitru
Fabricio Escobar-Jimenez, Ricardo
Hugo Olivares-Peregrino, Victor
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2016,
[9] Fahd J., 2018, Results Nonlinear Anal, V2, P88, DOI DOI 10.3934/DCDSS.2020039
[10] Fractal Derivative Model for Air Permeability in Hierarchic Porous Media
Fan, Jie
He, Jihuan
[J]. ABSTRACT AND APPLIED ANALYSIS, 2012,

← 1 2 →