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

Advances in Difference Equations

Ricardo Fabricio Escobar-Jimenez¹  Victor Fabian Morales-Delgado⁵  Jos Francisco Gmez-Aguilar⁹  Victor Hugo Olivares-Peregrino^1,10  Dumitru Baleanu^1,11  Huitzilin Ypez-Martnez^1,13 

[1] CONACYT-Centro Nacional de InvestigacióCentro Nacional de InvestigacióDepartment of Mathematics and Computer Sciences, Faculty of Art and Sciences, Cankaya University, Balgat, Turkey;Institute of Space Sciences, Bucharest, Romania;Unidad AcadéUniversidad Autógico Nacional de Mégico, Tecnolómica de Matemán y Desarrollo Tecnolónoma de Guerrero, Chilpancingo, Mexico;noma de la Ciudad de Méticas, Universidad Autóxico D.F., Mexico;xico, Cuernavaca, Mexico;xico, Mé

关键词: fractional calculus;    fractional differential equations;    Caputo fractional operator;    Caputo-Fabrizio fractional operator;    homotopy analysis method;    approximate solution;   

DOI  :  10.1186/s13662-016-0891-6

学科分类：数学（综合）

来源: SpringerOpen

【 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.

【 授权许可】

CC BY