New results on existence in the framework of Atangana–Baleanu derivative for fractional integro-differential equations

Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition

“…The main advantages of these operator is the freedom of choice of the function ψ and its merge and acquire the properties of the aforementioned fractional operators. Results based on these setting can be found in [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. The Ulam-Hyers stability point of view, is the vital and special type of stability that attracts many researchers in the field of mathematical analysis.…”

Applications of some fixed point theorems for fractional differential equations with Mittag-Leffler kernel

“…Many authors showed their interest in this definition as it holds the profits of Riemann-Liouville and Caputo derivatives [20][21][22][23][24][25][26][27][28][29][30]. Last year, Atangana et al provided the numerical approximation to the fractional advection-diffusion equation whose fractional derivatives are Atangana-Baleanu derivative of Riemann-Liouville type [14].…”

Existence of mild solutions for impulsive neutral Hilfer fractional evolution equations

“…Fractional differential equations (FDEs) are among the strongest tools of mathematical modeling and are successfully employed to model complex physical and biological phenomena like anomalous diffusion, viscoelastic behavior, power laws, and automatic remote control systems. In the available literature, notable definitions of fractional derivatives were given by famous mathematicians, but the most commonly used are the Riemann-Liouville (RL) and Caputo derivatives [1,2,21,22,24,26,29,39]. Thus FDEs involving the RL fractional derivative or Caputo derivative have considered frequently for investigating the existence of mild solutions.…”