On the existence of positive solutions for generalized fractional boundary value problems

The existence of positive solutions is established for boundary value problems defined within generalized Riemann–Liouville and Caputo fractional operators. Our approach is based on utilizing the technique of fixed point theorems. For the sake of converting the proposed problems into integral equations, we construct Green functions and study their properties for three different types of boundary value problems. Examples are presented to demonstrate the validity of theoretical findings.Scopu

Existence and Exponential Stability of Positive Almost Periodic Solutions for a Model of Hematopoiesis

By employing the contraction mapping principle and applying Gronwall-Bellman's inequality, sufficient conditions are established to prove the existence and exponential stability of positive almost periodic solution for nonlinear impulsive delay model of hematopoiesis.The research of Juan J. Nieto has been partially supported by Ministerio de Educacion y Ciencia and FEDER, project MTM2007-61724S

An LMI Approach-Based Mathematical Model to Control Aedes aegypti Mosquitoes Population via Biological Control

In this paper, a novel age-structured delayed mathematical model to control Aedes aegypti mosquitoes via Wolbachia-infected mosquitoes is introduced. To eliminate the deadly mosquito-borne diseases such as dengue, chikungunya, yellow fever, and Zika virus, the Wolbachia infection is introduced into the wild mosquito population at every stage. This method is one of the promising biological control strategies. To predict the optimal amount of Wolbachia release, the time varying delay is considered. Firstly, the positiveness of the solution and existence of both Wolbachia present and Wolbachia free equilibrium were discussed. Through linearization, construction of suitable Lyapunov–Krasovskii functional, and linear matrix inequality theory (LMI), the exponential stability is also analyzed. Finally, the simulation results are presented for the real-world data collected from the existing literature to show the effectiveness of the proposed model.This article has been written with the joint partial financial support of SERB-EEQ/2019/000365, the National Science Centre in Poland (Grant DEC-2017/25/B/ST7/02888, RUSA Phase 2.0 (Grant No. F 24–51/2014-U), Policy (TN Multi-Gen), Dept.of Edn. Govt. of India, UGC-SAP (DRS-I) (Grant No. F.510/8/DRS-I/2016(SAP-I)), DST-PURSE 2nd Phase programme vide letter No. SR/PURSE Phase 2/38 (G), DST (FIST—level I) 657876570 (Grant No. SR/FIST/MS-I/2018/17), and Prince Sultan University for funding this work through research group Nonlinear Analysis Methods in Applied Mathematics (NAMAM) group number RG-DES-2017-01-17

Oscillation results for a fractional partial differential system with damping and forcing terms

In this paper, we study the forced oscillation of solutions of a fractional partial differential system with damping terms by using the Riemann-Liouville derivative and integral. We obtained some new oscillation results by using the integral averaging technique. The obtained results are illustrated by using some examples

A STABILITY CRITERION FOR DELAY DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECTS

In this paper, we prove that if a delay differential equation with impulse effects of the form x ′ (t) = A(t)x(t) + B(t)x(t − τ) , t � = θi, ∆x(θi) = Cix(θi) + Dix(θi−j), i ∈ N, verifies a Perron condition then its trivial solution is uniformly asymptotically stable

Perron's theorem for linear impulsive differential equations with distributed delay

In this paper it is shown that under a Perron condition trivial solution of linear impulsive differential equation with distributed delay is uniformly asymptotically stable