Vieta–Fibonacci wavelets: Application in solving fractional pantograph equations
Hadis Azin, Mohammad Heydari, Fakhrodin Mohammadi
Abstract
In this paper, the Vieta–Fibonacci wavelets as a new family of orthonormal wavelets are generated. An operational matrix concerning fractional integration of these wavelets is extracted. A numerical scheme is established based on these wavelets and their fractional integral matrix together with the collocation technique to solve fractional pantograph equations. The presented method reduces solving the problem under study into solving a system of algebraic equations. Several examples are provided to show the accuracy of the method.
Topics & Concepts
WaveletMathematicsOrthonormal basisLegendre waveletAlgebraic equationFibonacci numberApplied mathematicsMatrix (chemical analysis)Mathematical analysisAlgebra over a fieldPure mathematicsWavelet transformDiscrete wavelet transformDiscrete mathematicsComputer scienceNonlinear systemArtificial intelligencePhysicsMaterials scienceComposite materialQuantum mechanicsFractional Differential Equations SolutionsDifferential Equations and Numerical MethodsNonlinear Differential Equations Analysis