Hybrid Rational Haar Wavelet and Block Pulse Functions Method for Solving Population Growth Model and Abel Integral Equations

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.

Gegenbauer wavelet quasi‐linearization method for solving fractional population growth model in a closed system

“…From Table 2, we infer that as the values of α increases, the attain solution of the proposed model increases and converge to the exact value at . Also, from Table 2, we found that our outcomes are sensibly better when contrasted with the outcomes acquired by 13,44 . The numerical outcomes propose that the nature of similar species population in a closed system relies upon the estimations of both α and κ .…”

“…Also, from Table 2, we found that our outcomes are sensibly better when contrasted with the outcomes acquired by. 13,44 The numerical outcomes propose that the nature of similar species population in a closed system relies upon the estimations of both 𝛼 and 𝜅. Finally, in Figure 8, we present the three-dimensional graphs of our approximate solution for distinct values of 𝜅.…”

Hybrid Pulse High-Frequency Voltage Injection Control Algorithm of Sensorless IPMSM for Vehicles

“…In this study, the polarity is identified by injecting pulse voltage into the hypothesized 􏽢 d axis. IPMSM transforms voltage and current components in the stationary coordinate system in accordance with Euler's theorem to yield the resultant vector equation [18][19][20][21][22][23][24][25], which is expressed as…”

Comparison of the Orthogonal Polynomial Solutions for Fractional Integral Equations

“…These equations occur in different fields of the sciences. The solution methods of the Abel integral equations are collocation methods [9][10][11][12][13], Adomian decomposition methods [14][15][16], homotopy perturbation methods [17], quadrature methods [18][19][20], homotopy analysis methods [21], and Laplace transform methods [22][23][24][25][26]. Besides, Abel integral equations are also solved by using Chebyshev [27][28][29], Legendre [30,31], Taylor [32], Bernstein [33,34], Block-Pulse [35], and Laguerre [36] functions.…”