Analysis of Keller-Segel model with Atangana-Baleanu fractional derivative

Abstract

The new definition of the fractional derivative was defined by Atangana and Baleanu in 2016. They used the generalized Mittag-Leffler function with the non-singular and non-local kernel. Further, their version provides all properties of fractional derivatives. Our aim is to analyse the Keller-Segel model with Caputo and Atangana-Baleanu fractional derivative in Caputo sense. Using fixed point theory, we first show the existence of coupled solutions. We then examine the uniqueness of these solutions. Finally, we compare our results numerically by modifying our model according to both definitions, and we demonstrate these results on the graphs in detail. All computations were done using Mathematica.

On a nonlinear Volterra integrodifferential equation involving fractional derivative with Mittag-Leffler kernel

“…Until now, to the best of our knowledge, the works on analysis existence and regularity for ODEs and PDEs with Atangana-Baleanu derivative is very limited. In [18], the authors show the existence of the Keller-Segel model with Caputo and Atangana-Baleanu fractional derivative using fixed point theory. In [24], the fractional logistic model concerned with Atangana-Baleanu fractional derivative is considered.…”

Hermite–Hadamard inequality for fractional integrals of Caputo–Fabrizio type and related inequalities

“…Fractional calculus has been appealing to many researchers over the last decades [1][2][3][4][5]. Some researchers have found that different fractional derivatives with different singular or nonsingular kernels need to be identified by real-world problems in different fields of engineering and science [6][7][8][9][10][11][12].…”

Boundedness of Fractional Integral Operators Containing Mittag-Leffler Function via Exponentially s-Convex Functions

“…Fractional integral operators are very useful in mathematical inequalities. e authors have established fractional integral inequalities due to different fractional integral operators, see [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Many authors have used Mittag-Leffler function to define fractional integral operators.…”