Laplace decomposition for solving nonlinear system of fractional order partial differential equations
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Date
2020
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Abstract
In the present article a modified decomposition method is implemented to solve systems of partial differential equations of fractional-order derivatives. The derivatives of fractional-order are expressed in terms of Caputo operator. The validity of the proposed method is analyzed through illustrative examples. The solution graphs have shown a close contact between the exact and LADM solutions. It is observed that the solutions of fractional-order problems converge towards the solution of an integer-order problem, which confirmed the reliability of the suggested technique. Due to better accuracy and straightforward implementation, the extension of the present method can be made to solve other fractional-order problems.
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Keywords
Caputo Operator, Adomian Decomposition Method, Laplace Transformation, Fractional Systems of Partial Differential Equations, Decomposition method (queueing theory), Economics, Biochemistry, Gene, Engineering, Differential equation, Ecology, Physics, Partial differential equation, Discrete mathematics, Programming language, Fractional Derivatives, Chemistry, Modeling and Simulation, Physical Sciences, Laplace transform, Caputo operator, Fractional Order Control, Operator (biology), Mathematical analysis, Quantum mechanics, QA1-939, FOS: Mathematics, Biology, Fractional systems of partial differential equations, Anomalous Diffusion Modeling and Analysis, Order (exchange), Analysis and Design of Fractional Order Control Systems, Decomposition, Laplace transformation, Extension (predicate logic), Fractional calculus, Statistical and Nonlinear Physics, Applied mathematics, Computer science, Physics and Astronomy, Control and Systems Engineering, FOS: Biological sciences, Nonlinear system, Repressor, Adomian decomposition method, Fractional Calculus, Integer (computer science), Transcription factor, Mathematics, Ordinary differential equation, Finance, Rogue Waves in Nonlinear Systems, fractional systems of partial differential equations, Fractional derivatives and integrals, Fractional partial differential equations, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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Fields of Science
01 natural sciences, 0103 physical sciences, 0101 mathematics
Citation
Khan, Hassan...et al. (2020). "Laplace decomposition for solving nonlinear system of fractional order partial differential equations", Advances in Difference Equations, Vol. 2020, No. 1.
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OpenCitations Citation Count
43
Source
Advances in Difference Equations
Volume
2020
Issue
1
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CrossRef : 37
Scopus : 59
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