Abstract: It is well known that integer-order neural networks with diffusion have rich spatial and temporal dynamical behaviors, including Turing pattern and Hopf bifurcation. Recently, some studies indicate that fractional calculus can depict the memory and hereditary

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Abstract: This paper concerned with a diffusive predator–prey model with fear effect. First, some basic dynamics of system is analyzed. Then based on stability analysis, we derive some conditions for stability and bifurcation of constant steady state. Furthermore, we d

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Abstract: In this paper, we consider the existence of infinitely many sign-changing solutions for an elliptic equation involving double critical Hardy–Sobolev–Maz’ya terms. By using a compactness result obtained in C.H. Wang, J. Yang, Infinitely many solutions for an e

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Abstract: This paper is concerned with the controllability problem for higher-order fractional damped stochastic systems with multiple delays, which involves fractional Caputo derivatives of any different orders. In the process of proof, we have proposed the controllab

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Abstract: In this paper, we extend a Leslie–Gower-type predator–prey system with ratio-dependent Holling III functional response considering the cost of antipredator defence due to fear. We study the impact of the fear effect on the model, and we find that many interes

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Abstract: In this paper, we deal with the existence of solutions for a coupled system of integral equations in the Cartesian product of weighted Sobolev spaces E = W 1,1(a, b) × W 1,1(a, b).The results were achieved by equipping the space with the vector-valued norms a

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Abstract: Oncolytic virotherapy is a therapy for the treatment of malignant tumours. In some undesirable cases, the injection of viral particles can lead to stationary oscillations, thus preventing the full destruction of the tumour mass. We investigate the oscillation

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Abstract: The present article intends to prove the existence of best proximity points (pairs) using the notion of measure of noncompactness. We introduce generalized classes of cyclic (noncyclic) F-contractive operators, and then derive best proximity point (pair) resu

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Abstract: In this article, we consider the existence and uniqueness of solutions for a class of initial value problems of fuzzy Caputo–Katugampola fractional differential equations and the stability of the corresponding fuzzy fractional differential equations. The disc

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Abstract: This article analyzes the dynamical evolution of a three-dimensional symmetric oscillator with a fractional Caputo operator. The dynamical properties of the considered model such as equilibria and its stability are also presented. The existence results and un

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