An Approach of Integral Equations in Complex-Valued b -Metric Space Using Commuting Self-Maps

This paper is aimed at establishing some unique common fixed point theorems in complex-valued b -metric space under the rational type contraction conditions for three self-mappings in which the one self-map is continuous. A continuous self-map is commutable with the other two self-mappings. Our results are verified by some suitable examples. Ultimately, our results have been utilized to prove the existing solution to the two Urysohn integral type equations. This application illustrates how complex-valued b -metric space can be used in other types of integral operators.

Nonsingular Integral-Type Dynamic Finite-Time Synchronization for Hyper-Chaotic Systems

In this study, the synchronization problem of chaotic systems using integral-type sliding mode control for a category of hyper-chaotic systems is considered. The proposed control method can be used for an extensive range of identical/non-identical master-slave structures. Then, an integral-type dynamic sliding mode control scheme is planned to synchronize the hyper-chaotic systems. Using the Lyapunov stability theorem, the recommended control procedure guarantees that the master-slave hyper-chaotic systems are synchronized in the existence of uncertainty as quickly as possible. Next, in order to prove the new proposed controller, the master-slave synchronization goal is addressed by using a new six-dimensional hyper-chaotic system. It is exposed that the synchronization errors are completely compensated for by the new control scheme which has a better response compared to a similar controller. The analog electronic circuit of the new hyper-chaotic system using MultiSIM is provided. Finally, all simulation results are provided using MATLAB/Simulink software to confirm the success of the planned control method.

An inverse source problem for a two terms time-fractional diffusion equation

In this paper, we consider an inverse problem for a linear heat equation involving two time-fractional derivatives, subject to a nonlocal boundary condition. We determine a source term independent of the space variable, and the temperature distribution with an over- determining function of integral type.

DHMM-Based Asynchronous Finite-Time Sliding Mode Control for Markovian Jumping Lur’e Systems

This paper is concerned with the asynchronous problem for a class of Markovian jumping Lur’s system (MJLSs) via sliding mode control (SMC) in continuous-time domain. Specifically, the discrete hidden Markovian model (DHMM) is employed to describe the nonsynchronization between the controller modes and the MJLSs modes. In particular, considering the nonlinearity of MJLSs, a novel Lur’e-integral-type sliding surface is constructed. In order to ensure the finite-time stability of sliding mode dynamics and the accessibility of the specified sliding surface, the asynchronous Lur’e-type SMC law of the detector mode is presented. Finally, an example of DC motor is provided to demonstrate the effectiveness of the proposed technique.