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- Fractional calculus (2)
- Framelets (2)
- Harmonic numerical analysis (2)
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- Volterra integral equations (2)
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- Wavelets (2)
- Atangana–Baleanu fractional derivative (1)
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- Tight framelets (1)
- Unitary extension principle (1)
- Weakly singular Volterra- Fredholm integral equations (1)
Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
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.
A Collocation Method Via The Quasi-Affine Biorthogonal Systems For Solving Weakly Singular Type Of Volterra-Fredholm Integral Equations, Mutaz Mohammad, Carlo Cattani
A Collocation Method Via The Quasi-Affine Biorthogonal Systems For Solving Weakly Singular Type Of Volterra-Fredholm Integral Equations, Mutaz Mohammad, Carlo Cattani
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© 2020 Faculty of Engineering, Alexandria University Tight framelet system is a recently developed tool in applied mathematics. Framelets, due to their nature, are widely used in the area of image manipulation, data compression, numerical analysis, engineering mathematical problems such as inverse problems, visco-elasticity or creep problems, and many more. In this manuscript we provide a numerical solution of important weakly singular type of Volterra - Fredholm integral equations WSVFIEs using the collocation type quasi-affine biorthogonal method. We present a new computational method based on special B-spline tight framelets and use it to introduce our numerical scheme. The method provides …
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 …
Applications Of Bi-Framelet Systems For Solving Fractional Order Differential Equations, Mutaz Mohammad, Carlo Cattani
Applications Of Bi-Framelet Systems For Solving Fractional Order Differential Equations, Mutaz Mohammad, Carlo Cattani
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© 2020 CSIRO Framelets and their attractive features in many disciplines have attracted a great interest in the recent years. This paper intends to show the advantages of using bi-framelet systems in the context of numerical fractional differential equations (FDEs). We present a computational method based on the quasi-affine bi-framelets with high vanishing moments constructed using the generalized (mixed) oblique extension principle. We use this system for solving some types of FDEs by solving a series of important examples of FDEs related to many mathematical applications. The quasi-affine bi-framelet-based methods for numerical FDEs show the advantages of using sparse matrices …
Explicit Determinantal Formula For A Class Of Banded Matrices, Yerlan Amanbek, Zhibin Du, Yogi Erlangga, Carlos M. Da Fonseca, Bakytzhan Kurmanbek, António Pereira
Explicit Determinantal Formula For A Class Of Banded Matrices, Yerlan Amanbek, Zhibin Du, Yogi Erlangga, Carlos M. Da Fonseca, Bakytzhan Kurmanbek, António Pereira
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© 2020 Yerlan Amanbek et al., published by De Gruyter 2020. In this short note, we provide a brief proof for a recent determinantal formula involving a particular family of banded matrices.