THE GENERALIZED GEGENBAUER-HUMBERTS WAVELET FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS - Alkhalissi, Jumana H. S.; Emiroglu, Ibrahim; Secer, Aydin; Bayram, Mustafa (VINCA INST NUCLEAR SCI, 2020)
In this paper we present a new method of wavelets, based on generalized Gegenbauer-Humberts polynomials, named generalized Gegenbauer-Humberts wavelets. The operational matrix of integration are derived. By using the proposed method converted linear and non-linear fractional differential equation a system of algebraic equations. In addition, discussed some examples to explain the efficiency and accuracy of the presented method.
Keywords: block-pulse functions; operational matrix or integration; the generalized Gegenbauer-Humberts polynomial; fractional calculus; orthogonal polynomials; Thermodynamics