Existence results of Atangana-Baleanu fractional integro-differential inclusions of Sobolev type

Exact traveling wave solutions for (2+1)-dimensional Konopelchenko-Dubrovsky equation by using the hyperbolic trigonometric functions methods

“…The multiple formulations of the Konopelchenko-Dubrovsky equation ( 1) have been investigated by several scholars by using more methodological approaches including the Sato theory and Hirota method [16], the Jacobi elliptic functions [17], the modified auxiliary equation technique [18], the truncated Painlevé expansion and the Möbious invariant form [19], the Hirota bilinear method with the aid of positive quartic-quadraticfunctions [20], the improved of the extended F-expansion method [21], the modified simplest equation and cubic B-spline schemes [22], the Hirota direct method and linear superposition principle [23] and the references mentioned therein. Integro-differential equations in the sense of partial or fractional differential equations have been investigated extensively by numerous researchers across the world using various methodologies such as [24][25][26][27][28][29][30][31][32][33]. The primary inspiration for presenting work is the lengthy history of solving mathematical problems by using analytical or semi-analytic techniques.…”

Results on fractional integrodifferential equations with fractional boundary conditions by using a special type of operators over general Banach spaces with bounded approximation numbers

“…In [22][23][24], the authors proposed a new explicit numerical scheme based on two-step Lagrange polynomial for solving nonlinear FDEs of AB derivative and also presented the error analysis. [18,34,35] has defined higherorder AB fractional operators and established some useful relations among the operators. Some recent progress on the existence of solutions to various higher-order nonlinear FDEs based on AB derivative with classical boundary conditions can be found in a series of papers.…”

Modelling Influenza A disease dynamics under Caputo-Fabrizio fractional derivative with distinct contact rates

“…In this regard, many mathematical models, including integer and fractional order, have been created in the literature for the detailed analysis of various diseases such as cancer cells [3][4][5], varicella zoster virus [6], COVID-19 [7][8][9], plant disease [10], diabetes [11], prey-predator model [12], Nipah virus [13], childhood diseases [14], and hepatitis B [15]. Additionally, several studies have also been conducted regarding fractional derivative applications in various fields, such as optimal control [16,17], fixed point theory [18][19][20], chaotic systems [21], and heat flow [22]. In the same way, a number of mathematical models developed in regard to influenza have attempted to contribute to the literature in this area.…”