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

被引：0
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作者：
Victor Fabian Morales-Delgado
José Francisco Gómez-Aguilar
Huitzilin Yépez-Martínez
Dumitru Baleanu
Ricardo Fabricio Escobar-Jimenez
Victor Hugo Olivares-Peregrino
机构：
[1] Universidad Autónoma de Guerrero,Unidad Académica de Matemáticas
[2] Tecnológico Nacional de México,CONACYT
[3] Universidad Autónoma de la Ciudad de México,Centro Nacional de Investigación y Desarrollo Tecnológico
[4] Cankaya University,Department of Mathematics and Computer Sciences, Faculty of Art and Sciences
[5] Institute of Space Sciences,Centro Nacional de Investigación y Desarrollo Tecnológico
[6] Tecnológico Nacional de México,undefined
来源：
Advances in Difference Equations | / 2016卷
关键词：
fractional calculus; fractional differential equations; Caputo fractional operator; Caputo-Fabrizio fractional operator; homotopy analysis method; approximate solution;
D O I：
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学科分类号：
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.
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