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Title
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Numerical solution of variable-order fractional integro-partial differential equations via Sinc collocation method based on single and double exponential transformations
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Type
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JournalPaper
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Keywords
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Variable-order fractional calculus, Integro-partial differential equations, Diffusion equation, Sinc function, Numerical analysis, Spline approximation, Convergence and error
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Abstract
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This paper addresses the numerical solution of the multi-dimensional variable-order fractional integro-partial differential equations. The upwind scheme and a piecewise linear interpolation, are proposed to approximate the Coimbra variable-order fractional derivatives and integral term with kernel, respectively. Two new approaches via the Sinc collocation method based on single and double exponential transformations are adopted for the temporal and spatial discretizations, respectively. The convergence behaviour of the methods is analysed and the error bounds are provided. In addition, four test problems illustrate the validity and effectiveness of the proposed algorithms.
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Researchers
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Jose Antonio Tenreiro Machado (Fourth Researcher), ُSeddighe Banihashemi (Third Researcher), Behrouz Parsa Moghaddam (Second Researcher), Afshin Babaei (First Researcher)
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