Abstract
ABSTRACTThe Chebyshev Wavelet Method (CWM) is applied to evaluate the numerical solutions of some systems of linear fractional Voltera integro differential equations (FVIDEs). The applicability and validity of the proposed method is ensured by discussing some illustrative examples. The numerical results obtained by this technique are compared with the exact solutions of the problems. The error analysis reveals that the accuracy of the present method is higher than any existing numerical method.
Highlights
The theory and applications of fractional calculus can be observed in many fields of science and engineering such as nonlinear oscillation of earth quakes [1], fluid dynamic traffic [2] and signal processing [3]
Chebyshev wavelet method (CWM) In this paper, we consider the fractional systems of Volterra integro differential equations x y(m)(x) = f (x)+ k(x, t, y1(m), y2(m), y3(m), . . . , yn(m))dt, where f (x) = [f1(x), f2(x), . . . , fn(x)]T
Cn,mψn,m(x), y2k,M(x) dn,mψn,m(x), ynk,M(x) en,mψn,m(x), (5). This implies that there are 2k−1M × 2k−1M . . . n − time . . . × 2k−1M conditions to determine 2k−1M × 2k−1M . . . n − time . . . × 2k−1M coefficients ci,j, di,j, . . . , ei,j. We put these coefficients in Equation (5) to obtain the approximate solution by Chebyshev Wavelet method (CWM)
Summary
The theory and applications of fractional calculus can be observed in many fields of science and engineering such as nonlinear oscillation of earth quakes [1], fluid dynamic traffic [2] and signal processing [3]. The authors have used different numerical techniques to find the approximate solution of fractional differential and integral equations such as Adomian Decomposition Method (ADM) [4], Spline Collocation Method (SCM) [5], Fractional Transform Method (FTM) [6], Homotopy Perturbation Method (HPM) [7], Operational Tau Method (OTM) [8], Shifted Chebyshev Polynomial Method (SCPM) [9], Rationalized Haar Functions Method (RHFM) [10] and Reproducing Kernel Hilbert Space (RKHSM) [11,12]. The numerical results found by the present method are compared with exact solution of the problem, showing the greatest degree accuracy
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