Analysis of non-homogeneous heat model with new trend of derivative with fractional order

被引：108

作者：

Alkahtani, Badr Saad T. ^{[1
]}

Atangana, Abdon ^{[2
]}

机构：

[1] King Saud Univ, Coll Sci, Dept Math, POB 1142, Riyadh 11989, Saudi Arabia

[2] Univ Orange Free State, Fac Nat & Agr Sci, Inst Groundwater Studies, ZA-9301 Bloemfontein, South Africa

来源：

CHAOS SOLITONS & FRACTALS | 2016年 / 89卷

关键词：

New trend of fractional derivative; Nonlinear heat; Existence and uniqueness; EQUATIONS;

D O I：

10.1016/j.chaos.2016.03.027

中图分类号：

O1 [数学];

学科分类号：

070101 [基础数学];

摘要：

The model of nonlinear heat was generalized using the new trend of derivative with fractional order. The new definition of derivative with fractional order has no singular kernel thus allows a description of the variation on time or space from the lower to the upper boundaries within the space/time interval which the investigation is taken place for a given model. In detail, we presented the analysis of unique and existence of a solution for the nonlinear fractional equation. We present the derivation of a special solution using an iterative method. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：566 / 571

页数：6

共 22 条

[1]

[Anonymous], APPL MATH NONLINEAR

[2]

Atangana A, 2016, J ENG MECH, DOI 10.161/(ASCE).1943.7889.0001091

[3]

On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation [J].

Atangana, Abdon .

APPLIED MATHEMATICS AND COMPUTATION, 2016, 273 :948-956

[4]

Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel [J].

Atangana, Abdon ;

Jose Nieto, Juan .

ADVANCES IN MECHANICAL ENGINEERING, 2015, 7 (10) :1-7

[5]

Analysis of the Keller-Segel Model with a Fractional Derivative without Singular Kernel [J].

Atangana, Abdon ;

Alkahtani, Badr Saad T. .

ENTROPY, 2015, 17 (06) :4439-4453

[6]

Application of a fractional advection-dispersion equation [J].

Benson, DA ;

Wheatcraft, SW ;

Meerschaert, MM .

WATER RESOURCES RESEARCH, 2000, 36 (06) :1403-1412

[7]

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-&

[8]

Caputo M., 2015, Progress Fract. Diff. Appl, V1, P73, DOI DOI 10.12785/PFDA/010201

[9]

Costamagna A, 2016, APPL MATH NONLINEAR, V1, P207

[10]

A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type [J].

Crank, J ;

Nicolson, P .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 1996, 6 (3-4) :207-226

← 1 2 3 →