A computational approach for solving fractional Volterra integral equations based on two-dimensional Haar wavelet method
Zohreh Abdollahi, M. Mohseni Moghadam, Habibollah Saeedi, M. J. Ebadi
Abstract
In this paper, an operational matrix (OM) method based on two-dimensional Haar wavelets (2D-HWs) is proposed for solving generalized 2D fractional Volterra integral equations (2D-FVIEs). The proposed method converts these equations into an algebraic equations system. Presenting theorems, we prove the existence and uniqueness of the mentioned equations and estimate the error bound for function approximation. Our method validity and applicability are demonstrated through some examples.
Topics & Concepts
MathematicsVolterra integral equationAlgebraic equationHaarUniquenessHaar waveletIntegral equationWaveletApplied mathematicsMatrix (chemical analysis)Mathematical analysisWavelet transformDiscrete wavelet transformNonlinear systemComputer scienceMaterials scienceArtificial intelligenceComposite materialQuantum mechanicsPhysicsFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsMathematical functions and polynomials