Solving PDEs of fractional order using the unified transform method

被引：48

作者：

Fernandez, Arran ^{[1
]}

Baleanu, Dumitru ^{[2
,3
]}

Fokas, Athanassios S. ^{[1
,4
]}

机构：

[1] Univ Cambridge, Dept Appl Math & Theoret Phys, Wilberforce Rd, Cambridge CB3 0WA, England

[2] Cankaya Univ, Dept Math, TR-06530 Ankara, Turkey

[3] Inst Space Sci, Bucharest, Romania

[4] Univ Southern Calif, Viterbi Sch Engn, Los Angeles, CA 90089 USA

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 339卷

基金：

英国工程与自然科学研究理事会;

关键词：

Fractional calculus; Partial differential equations; Fractional differential equations; Fokas method; PARTIAL-DIFFERENTIAL-EQUATIONS; RIEMANN-HILBERT APPROACH; HALF-LINE; MATHEMATICAL PHYSICS; CALCULUS;

D O I：

10.1016/j.amc.2018.07.061

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the unified transform method, also known as the Fokas method, for solving partial differential equations. We adapt and modify the methodology, incorporating new ideas where necessary, in order to apply it to solve a large class of partial differential equations of fractional order. We demonstrate the applicability of the method by implementing it to solve a model fractional problem. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：738 / 749

页数：12

共 32 条

[1] Fractional variational calculus in terms of Riesz fractional derivatives [J].