In this paper, we study a modified extragradient method for computing a common solution to the split equilibrium problem and fixed point problem of a nonexpansive semigroup in real Hilbert spaces. The weak and strong convergence characteristics of the proposed algorithm are investigated by employing suitable control conditions in such a setting of spaces. As a consequence, we provide a simplified analysis of various existing results concerning the extragradient method in the current literature. We also provide a numerical example to strengthen the theoretical results and the applicability of the proposed algorithm.

In this paper, we study the local and global existence, and uniqueness of mild solution to initial value problems for fractional semilinear evolution equations with compact and noncompact semigroup in Banach spaces. In particular, we derive the form of fundamental solution in terms of semigroup induced by resolvent and ψ-function from Caputo fractional derivatives. These results generalize previous work where the classical Caputo fractional derivative is considered. Moreover, we prove the Mittag-Leffler-Ulam-Hyers stability result. Finally, we give examples of time-fractional heat equation to illustrate the result.

We consider fractional hybrid differential equations involving the Caputo fractional derivative of order 0 < α < 1. Using fixed point theorems developed by Dhage et al. in Applied Mathematics Letters 34, 76-80 (2014), we prove the existence and approximation of mild solutions. In addition, we provide a numerical example to illustrate the results obtained. Primary 34A08; secondary 34A38; 34A45 MSC:

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Pest management, based on biological control, has drawn attention from several research groups, due to the exclusion of chemical pesticides, which have debilitating outcomes, both on the environment and human health. Biological pest control policies have been determined using the model-based control approach. In this study, the tensor product model transformation (TPMT) was applied to model the nonlinear dynamic of the biological pest control system. Consequently, the feedback control law representing the biological pest control policy was synthesized based on LMI. Under the designed controller, the pest population was regulated based on the desired level. The simulation of the biological pest control system was presented to confirm the performance of the designed control law. It is evident, that the feedback control method based on TPMT can be employed appropriately, in this application.

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