Abstract
We use a computational method based on rational Haar wavelet for solving nonlinear fractional integro-differential equations. To this end, we apply the operational matrix of fractional integration for rational Haar wavelet. Also, to show the efficiency of the proposed method, we solve particularly population growth model and Abel integral equations and compare the numerical results with the exact solutions.
Highlights
Fractional calculus is a field of applied mathematics that deals with derivatives and integrals of arbitrary orders
A large class of dynamical systems appearing throughout the field of engineering and applied mathematics is described by fractional differential equations
We presented a numerical scheme for solving fractional population growth model and Abel integral equations of the first and second kinds
Summary
Fractional calculus is a field of applied mathematics that deals with derivatives and integrals of arbitrary orders (including complex orders). Many authors applied operational matrices of integration and derivative to reduce the original problem into an algebraic one. According to this fact that the orthogonal polynomials play an important role to solve integral and differential equations, many researchers constructed operational matrix of fractional and integer derivatives for some types of these polynomials, such as Flatlet oblique multiwavelets [17, 18], B-spline cardinal functions [19], Legendre polynomials, Chebyshev polynomials, and CAS wavelets [20].
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