Solving a System of Fractional-Order Volterra-Fredholm Integro-Differential Equations with Weakly Singular Kernels via the Second Chebyshev Wavelets Method
Esmail Bargamadi, Leila Torkzadeh, Kazem Nouri, Amin Jajarmi
Abstract
In this paper, by means of the second Chebyshev wavelet and its operational matrix, we solve a system of fractional-order Volterra–Fredholm integro-differential equations with weakly singular kernels. We estimate the functions by using the wavelet basis and then obtain the approximate solutions from the algebraic system corresponding to the main system. Moreover, the implementation of our scheme is presented, and the error bounds of approximations are analyzed. Finally, we evaluate the efficiency of the method through a numerical example.
Topics & Concepts
MathematicsChebyshev equationWaveletChebyshev filterChebyshev polynomialsChebyshev iterationChebyshev nodesAlgebraic equationApplied mathematicsOrder (exchange)Differential equationMatrix (chemical analysis)Fractional calculusMathematical analysisFredholm integral equationIntegral equationNonlinear systemComputer scienceOrthogonal polynomialsClassical orthogonal polynomialsEconomicsQuantum mechanicsFinanceArtificial intelligenceMaterials sciencePhysicsComposite materialFractional Differential Equations SolutionsDifferential Equations and Numerical MethodsIterative Methods for Nonlinear Equations