A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative

Abstract

We present a fractional-order model for the COVID-19 transmission with Caputo-Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We prove the existence of a unique solution and the stability of the iteration approach by using fixed point theory. We also present numerical results to simulate virus transmission and compare the results with those of the Caputo derivative.

An increasing variables singular system of fractional q-differential equations via numerical calculations

“…with boundary value conditions k 1 (0) = 2 3 , . Now, we check (23) and (24). For each t ∈ J and (k 1 , k 2 , .…”

“…Later, qfractional boundary value problems have been considered by many researchers (see, for example, [6][7][8][9][10][11][12][13]). Nowadays many researchers focus on applications of fractional calculus [14][15][16][17][18][19][20][21][22][23][24][25] or analytical studies [26][27][28][29][30][31][32][33][34][35][36]. via boundary conditions k (i) (0) = l (i) (0) = 0 for 0 ≤ i ≤ n -2, D δ 1 0 + [k](1) = 0 for 2 < δ 1 < n -1, σ 1δ 1 ≥ 1, and D δ 2 0 + [l](1) = 0 for 2 < δ 2 < n -1, σ 2δ 2 ≥ 1, where n ≥ 4, n -1 < σ i < n, 0 < α i < 1, 1 < β ij < 2 for i = 1, 2 and j = 1, 2, .…”

SEIR epidemic model for COVID-19 transmission by Caputo derivative of fractional order

“…In recent years, many papers have been published on the subject of Caputo-Fabrizio fractional derivative (see, for example, [24][25][26][27][28][29][30]). Mathematical models are used to simulate the transmission of coronavirus (see, for example, [31][32][33][34][35][36][37]).…”

Topological degree theory and Caputo–Hadamard fractional boundary value problems

“…Instances of the application of such fractional operators can be found in various sciences such as biomathematics, electrical circuits, medicine, etc. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. All of these reasons have led researchers to find many aspects of the structure of the fractional boundary value problems and the hereditary properties of their solutions.…”