ArticleEntropy (Basel, Switzerland)2020
An Efficient Method Based on Framelets for Solving Fractional Volterra Integral Equations.
Article in Entropy (Basel, Switzerland), 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed.
- The dynamics of COVID-19 in the UAE based on fractional derivative modeling using Riesz wavelets simulation.Advances in difference equations · 2021Article
- On the dynamical modeling of COVID-19 involving Atangana-Baleanu fractional derivative and based on Daubechies framelet simulations.Chaos, solitons, and fractals · 2020Article
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Abstract
This paper is devoted to shedding some light on the advantages of using tight frame systems for solving some types of fractional Volterra integral equations (FVIEs) involved by the Caputo fractional order derivative. A tight frame or simply framelet, is a generalization of an orthonormal basis. A lot of applications are modeled by non-negative functions; taking this into account in this paper, we consider framelet systems generated using some refinable non-negative functions, namely, B-splines. The FVIEs we considered were reduced to a set of linear system of equations and were solved numerically based on a collocation discretization technique. We present many important examples of FVIEs for which accurate and efficient numerical solutions have been accomplished and the numerical results converge very rapidly to the exact ones.
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