Abstract
This research work addresses the numerical solutions of nonlinear fractional integro-differential equations with mixed boundary conditions, using Chebyshev wavelet method. The basic idea of this work started from the Caputo definition of fractional differential operator. The fractional derivatives are replaced by Caputo operator, and the solution is approximated by wavelet family of functions. The numerical scheme by Chebyshev wavelet method is constructed through a very simple and straightforward way. The numerical results of the current method are compared with the exact solutions of the problems, which show that the proposed method has a strong agreement with the exact solutions of the problems. The numerical solutions of the present method are also compared with steepest decent method and Adomian decomposition method. The comparison with other methods reveals that this method has the highest degree of accuracy than those methods.
Highlights
Many important problems in fluid mechanics, viscoelasticity, electromagnetic, and other fields of science and engineering are modeled by fractional differential and integral equations.[1,2] Due to the real facts of its applications in different areas of research, the researchers have taken keen interest in the study of fractional calculus
We have considered some initial and mixed boundary value fractional integro-differential equations of order less than one
We show that the numerical results obtained by Chebyshev wavelet method (CWM) are highly accurate than the result of Adomian decomposition method (ADM)
Summary
Many important problems in fluid mechanics, viscoelasticity, electromagnetic, and other fields of science and engineering are modeled by fractional differential and integral equations.[1,2] Due to the real facts of its applications in different areas of research, the researchers have taken keen interest in the study of fractional calculus. Keywords Chebyshev wavelet method, fractional integro-differential equations, nonlinear problems, wavelet techniques, fractional calculus Many researchers have tried their best to use different techniques to find the analytical and numerical solutions of these problems, for example, Adomian decomposition method (ADM),[5] spline collocation An efficient CWM is used to obtain the numerical solutions of some Volterra–Fredholm fractional integro-differential equations. The Caputo definition of fractional differential operator is given by ðt ðDmgÞðtÞ = 1 Gðn À mÞ
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