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An Efficient Method Based on Framelets for Solving Fractional Volterra Integral Equations

1
Department of Mathematics & Statistics, Zayed University, Abu Dhabi 144543, UAE
2
Department of Computer Technology and Systems, Kuban State Agrarian University, Krasnodar 350044, Russia
3
Engineering School (DEIM), Tuscia University, 01100 Viterbo, Italy
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(8), 824; https://doi.org/10.3390/e22080824
Received: 9 July 2020 / Revised: 17 July 2020 / Accepted: 18 July 2020 / Published: 28 July 2020
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines II)
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. View Full-Text
Keywords: framelets; numerical solution; fractional calculus; generalization of Unequal Error Protection (UEP); wavelets; harmonic numerical analysis; volterra integral equations framelets; numerical solution; fractional calculus; generalization of Unequal Error Protection (UEP); wavelets; harmonic numerical analysis; volterra integral equations
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MDPI and ACS Style

Mohammad, M.; Trounev, A.; Cattani, C. An Efficient Method Based on Framelets for Solving Fractional Volterra Integral Equations. Entropy 2020, 22, 824. https://doi.org/10.3390/e22080824

AMA Style

Mohammad M, Trounev A, Cattani C. An Efficient Method Based on Framelets for Solving Fractional Volterra Integral Equations. Entropy. 2020; 22(8):824. https://doi.org/10.3390/e22080824

Chicago/Turabian Style

Mohammad, Mutaz; Trounev, Alexander; Cattani, Carlo. 2020. "An Efficient Method Based on Framelets for Solving Fractional Volterra Integral Equations" Entropy 22, no. 8: 824. https://doi.org/10.3390/e22080824

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