Laplace homotopy analysis method for solving linear partial differential equations using a fractional derivative with and without kernel singular

被引：100

作者：

Fabian Morales-Delgado, Victor ^{[1
]}

Francisco Gomez-Aguilar, Jose ^{[2
]}

Yepez-Martinez, Huitzilin ^{[3
]}

Baleanu, Dumitru ^{[4
,5
]}

Fabricio Escobar-Jimenez, Ricardo ^{[6
]}

Hugo Olivares-Peregrino, Victor ^{[6
]}

机构：

[1] Univ Autonoma Guerrero, Unidad Acad Matemat, Ave Lazaro Cardenas S-N, Chilpancingo, Guerrero, Mexico

[2] Tecnol Nacl Mexico, CONACYT Ctr Nacl Invest & Desarrollo Tecnol, Interior Internado Palmira S-N, Cuernavaca 62490, Morelos, Mexico

[3] Univ Autonoma Ciudad Mexico, Prolongac San Isidro 151, Mexico City 09790, DF, Mexico

[4] Cankaya Univ, Fac Art & Sci, Dept Math & Comp Sci, TR-0630 Ankara, Turkey

[5] Inst Space Sci, POB MG-23, Bucharest 76900, Romania

[6] Tecnol Nacl Mexico, Ctr Nacl Invest & Desarrollo Tecnol, Interior Internado Palmira S-N, Cuernavaca 62490, Morelos, Mexico

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2016年

关键词：

fractional calculus; fractional differential equations; Caputo fractional operator; Caputo-Fabrizio fractional operator; homotopy analysis method; approximate solution; SYSTEM; SCHEME; MODEL;

D O I：

10.1186/s13662-016-0891-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, we present an analysis based on a combination of the Laplace transform and homotopy methods in order to provide a new analytical approximated solutions of the fractional partial differential equations (FPDEs) in the Liouville-Caputo and Caputo-Fabrizio sense. So, a general scheme to find the approximated solutions of the FPDE is formulated. The effectiveness of this method is demonstrated by comparing exact solutions of the fractional equations proposed with the solutions here obtained.

引用

页数：17

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