Francisco Gomez-Aguilar, JoseYepez-Martinez, HuitzilinBaleanu, DumitruFabricio Escobar-Jimenez, RicardoHugo Olivares-Peregrino, VictorFabian Morales-Delgado, Victor2018-09-252025-09-182018-09-252025-09-182016Baleanu, D...[et.al.]. (2016). Laplace homotopy analysis method for solving linear partial differential equations using a fractional derivative with and without kernel singular. Advances In Difference Equations. http://dx.doi.org/10.1186/s13662-016-0891-61687-1847https://doi.org/10.1186/s13662-016-0891-6https://hdl.handle.net/20.500.12416/12693Yepez-Martinez, Huitzilin/0000-0002-8532-5669; Escobar Jimenez, Ricardo Fabricio/0000-0003-3367-6552; Gomez-Aguilar, J.F./0000-0001-9403-3767; Olivares Peregrino, Victor Hugo/0000-0002-5214-4984In 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.eninfo:eu-repo/semantics/openAccessFractional CalculusFractional Differential EquationsCaputo Fractional OperatorCaputo-Fabrizio Fractional OperatorHomotopy Analysis MethodApproximate SolutionArticle10.1186/s13662-016-0891-62-s2.0-84976516176