Numerical solutions of fractional parabolic equations with generalized Mittag-Leffler kernels

被引：16

作者：

Alomari, Abedel-Karrem ^{[1
]}

Abdeljawad, Thabet ^{[2
,3
,4
]}

Baleanu, Dumitru ^{[5
,6
]}

Saad, Khaled M. ^{[7
,8
]}

Al-Mdallal, Qasem M. ^{[9
]}

机构：

[1] Yarmouk Univ, Fac Sci, Dept Math, Irbid, Jordan

[2] Prince Sultan Univ, Dept Math & Gen Sci, Riyadh, Saudi Arabia

[3] China Med Univ, Dept Med Res, Taichung, Taiwan

[4] Asia Univ, Dept Comp Sci & Informat Engn, Taichung, Taiwan

[5] Cankaya Univ, Fac Arts & Sci, Dept Math, Ankara, Turkiye

[6] Inst Space Sci, Magurele, Romania

[7] Najran Univ, Coll Arts & Sci, Dept Math, Najran, Saudi Arabia

[8] Taiz Univ, Fac Sci Appl, Dept Math, Taizi, Yemen

[9] United Arab Emirates Univ, Dept Math Sci, Abu Dhabi, U Arab Emirates

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2024年 / 40卷 / 01期

关键词：

Homotopy analysis method; Mittag– Lefller kernel; time fractional parabolic nonlinear equation; CAPUTO-FABRIZIO; MODEL; DERIVATIVES; DIFFUSION; SYSTEMS; RC;

D O I：

10.1002/num.22699

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we investigate the generalized fractional operator Caputo type (ABC) with kernels of Mittag-Lefller in three parameters E alpha,mu gamma(lambda t) and its fractional integrals with arbitrary order for solving the time fractional parabolic nonlinear equation. The generalized definition generates infinitely many problems for a fixed fractional derivative alpha. We utilize this operator with homotopy analysis method for constructing the new scheme for generating successive approximations. This procedure is used successfully on two examples for finding the solutions. The effectiveness and accuracy are verified by clarifying the convergence region in the PLANCK CONSTANT OVER TWO PI-curves as well as by calculating the residual error and the results were accurate. Based on the experiment, we verify the existence of the solution for the new parameters. Depending on these results, this treatment can be used to find approximate solutions to many fractional differential equations.

引用

页数：13