Laplace Homotopy Analysis Method for Solving Linear Partial Differential Equations Using a Fractional Derivative With and Without Kernel Singular
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Date
2016
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Publisher
Springeropen
Open Access Color
GOLD
Green Open Access
No
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No
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Top 1%
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Top 10%
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Top 1%
Abstract
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.
Description
Yepez-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/0000-0002-5214-4984
Keywords
Fractional Calculus, Fractional Differential Equations, Caputo Fractional Operator, Caputo-Fabrizio Fractional Operator, Homotopy Analysis Method, Approximate Solution, Laplace transform, Mathematical analysis, Convergence Analysis of Iterative Methods for Nonlinear Equations, Engineering, Differential equation, Green's function for the three-variable Laplace equation, Laplace's equation, FOS: Mathematics, Anomalous Diffusion Modeling and Analysis, Laplace transform applied to differential equations, Numerical Analysis, Algebra and Number Theory, Applied Mathematics, Fractional calculus, Pure mathematics, Partial differential equation, Derivative-Free Methods, Applied mathematics, Fracture Mechanics Modeling and Simulation, Fractional Derivatives, Homotopy analysis method, Mechanics of Materials, Modeling and Simulation, Physical Sciences, Kernel (algebra), Homotopy Analysis Method, Homotopy, Analysis, Mathematics, Ordinary differential equation, Fractional ordinary differential equations, fractional calculus, Caputo-fabrizio fractional operator, Fractional derivatives and integrals, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, Theoretical approximation of solutions to ordinary differential equations, homotopy analysis method, fractional differential equations, Caputo fractional operator, Fractional partial differential equations, approximate solution
Fields of Science
01 natural sciences, 0103 physical sciences
Citation
Baleanu, 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/s13662-016-0891-6
WoS Q
Q1
Scopus Q
OpenCitations Citation Count
90
Source
Advances in Difference Equations
Volume
2016
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Citations
CrossRef : 46
Scopus : 110
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Mendeley Readers : 25
SCOPUS™ Citations
114
checked on Feb 25, 2026
Web of Science™ Citations
102
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