Controllability of neutral impulsive fractional differential equations with Atangana-Baleanu-Caputo derivatives

New exploration on approximate controllability of fractional neutral‐type delay stochastic differential inclusions with non‐instantaneous impulse

“…Controllability is the qualitative property of the dynamical control system which shows the existence of a control function which can steer the dynamical system from an initial state to any desired final state. In recent years, many researchers have extensively investigated controllability results for various dynamical systems [4,8,[12][13][14][15][16]. Furthermore, the deterministic models often experience variations that are random, or that at least look to be random due to environmental noise.…”

“…Its potential applications have gained a lot of importance. In the last few decades, the growth of science and engineering systems has considerably stimulated the employment of fractional calculus in various areas of the control theory, for example, in controllability, fault estimation, observability, observer design, stability, and stabilization [12,14,16,[20][21][22]. Fractional derivatives are divided into two major types; singular kernels such as the Riemann-Liouville and Caputo [22] and Hilfer derivatives [23] and nonsingular kernels such as the Caputo-Fabrizio [24] and the Atangana-Baleanu fractional derivatives [25].…”

A note concerning to approximate controllability of Atangana–Baleanu fractional neutral stochastic integro‐differential system with infinite delay

“…Recently, Kumar et al 39 discussed the existence of a mild solution of the Atangana–Baleanu fractional differential system with noninstantaneous impulses. Bedi et al 40 studied the controllability results for fractional differential equations of neutral type with ABC derivatives. Recently, Williams et al 41 iscussed the results on AB fractional equation via fixed point method.…”

Solution of fractional Sawada–Kotera–Ito equation using Caputo and Atangana–Baleanu derivatives

“…This new ABC derivative has a great memory due to the existence of Mittag–Leffler function as its nonlocal kernel; eventually, it results in a better comparative performance as compared to other existing fractional derivative operators. Validation of the above claim is justified by applying ABC operator, instead of other operators, and solving various scientific models, namely, the general sequential hybrid class of FDEs [15, 16], controllability of neutral impulsive [17], Covid‐19 mathematical model [18, 19], fractional typhoid model [20], wireless sensor network as an application of the fuzzy fractional SIQR model [21], plasma particle model with circular LASER light polarization [22], Hepatitis B model [23], SEIR and blood coagulation technologies [24], a fractal‐fractional tuberculosis [25] and tobacco [26] mathematical model, a class of population growth model [27], and the fractional nonlinear logistic system [27].…”