Numerical solutions for systems of fractional order differential equations with Bernoulli wavelets

Shifted-Chebyshev-polynomial-based numerical algorithm for fractional order polymer visco-elastic rotating beam

“…Compared with the former, the polynomial approximation method of fractional differential equations is particularly significant because of its fast speed, high efficiency and high precision. Polynomial approximation methods include Legendre polynomial method [31,32], Chebyshev wavelet method [33,34], Bernoulli wavelet method [35], Bernstein polynomial method [36,37] and shifted Chebyshev polynomials (SCPs) method [38]. The SCPs method can be used to approximate the unknown function on the extended interval, which makes it easier to solve the fractional differential equations with different physical mechanisms governing and historical background [39][40][41][42].…”

Analysis through the FDE Mathematical Model with Multiple Orders the Effects of the Specific Immune System Cells and the Multiple Antibiotic Treatment against Infection

“…In this section, the values obtained from the literature to the parameters used in the system (1) are given. The qualitative analysis of the proposed model was supported by numerical simulations.…”

“…If the stability conditions of these equilibrium points with respect to Table 2. is considered, then it is obtained that 0 is unstable due to ⏟ 220000000 > 0, 1 For six months of treatment, the special immune system cells, the susceptible Mycobacterium Tuberculosis population and the resistant Mycobacterium Tuberculosis population approach to the values 0.5289575, 0 and 1750, respectively.…”

“…Schematic representation of the interaction among bacteria, immune system cells and antibiotic concentrations according to the parameters used in(1). Let = 1,2,3, … , + 3.…”

Chebyshev wavelets operational matrices for solving nonlinear variable-order fractional integral equations

“…Many applied problems with memory can be successfully modeled via a fractional system of differential and/or integral equations, for example, semi-conductor devices [24], population dynamics [25], and identification of memory kernels in heat conduction [26]. During last years, several numerical techniques have been applied for solving fractional systems of differential and integral equations, for example, fractional power Jacobi spectral method [27], Bernoulli wavelets method [28], Haar wavelets method [29], Müntz-Legendre wavelets method [30], Block pulse functions method [31], finite difference method [32], spline collocation method [33][34][35], and spectral method [36].…”