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Fractional Nonlinear Volterra–Fredholm Integral Equations Involving Atangana–Baleanu Fractional Derivative: Framelet Applications, Mutaz Mohammad, Alexander Trounev
Fractional Nonlinear Volterra–Fredholm Integral Equations Involving Atangana–Baleanu Fractional Derivative: Framelet Applications, Mutaz Mohammad, Alexander Trounev
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© 2020, The Author(s). In this work, we propose a framelet method based on B-spline functions for solving nonlinear Volterra–Fredholm integro-differential equations and by involving Atangana–Baleanu fractional derivative, which can provide a reliable numerical approximation. The framelet systems are generated using the set of B-splines with high vanishing moments. We provide some numerical and graphical evidences to show the efficiency of the proposed method. The obtained numerical results of the proposed method compared with those obtained from CAS wavelets show a great agreement with the exact solution. We confirm that the method achieves accurate, efficient, and robust measurement.
An Efficient Method Based On Framelets For Solving Fractional Volterra Integral Equations, Mutaz Mohammad, Alexander Trounev, Carlo Cattani
An Efficient Method Based On Framelets For Solving Fractional Volterra Integral Equations, Mutaz Mohammad, Alexander Trounev, Carlo Cattani
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© 2020 by the authors. 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 …