Search

In this paper, we establish the existence and uniqueness of the solution to fractional equations abstract integrodifferential equation with impulsive as d η w (z) d z η + ζ w (z) = f (z , w (z)) + K (w) (z) , z > z 0 , z ≠ z k , 0 < η ≤ 1 , Δ w | z = z k = I k (w (z k -)) , k = 1 ,... , m , w (z 0) + φ (w) = w 0 ∈ X , where K (w) (z) = ∫ z 0 z q (z - s) g (s , w (s)) d s , and we used the fixed point theorems due to Banach space. The main conclusion is obtained by using fractional calculus, operator semigroup and fixed point theorem. Finally, in support, an example is presented to validate the obtained results. [ABSTRACT FROM AUTHOR]

This paper studies the drive-response synchronization for quaternion-valued shunting inhibitory cellular neural networks (QVSICNNs) with mixed delays. First, QVSICNN is decomposed into an equivalent real-valued system in order to avoid the non-commutativity of the multiplicity. Then, the existence of almost periodic solutions is obtained based on the Banach fixed point theorem. An novel state-feedback controller is designed to ensure the global exponential almost periodic synchronization. At the end of the paper, an example is given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

We establish, the existence and uniqueness of solutions to a class of Atangana-Baleanu (AB) derivative-based nonlinear fractional integro-differential equations with fractional boundary conditions by using special type of operators over general Banach and Hilbert spaces with bounded approximation numbers. The Leray-Schauder alternative theorem guarantees the existence solution and the Banach contraction principle is used to derive uniqueness solutions. Furthermore, we present an implicit numerical scheme based on the trapezoidal method for obtaining the numerical approximation to the solution. To illustrate our analytical and numerical findings, an example is provided and concluded in the final section. [ABSTRACT FROM AUTHOR]