On solvability of BVP for a coupled Hadamard fractional systems involving fractional derivative impulses

Abstract

<abstract><p>Hadamard fractional calculus is one of the most important fractional calculus theories. Compared with a single Hadamard fractional order equation, Hadamard fractional differential equations have a more complex structure and a wide range of applications. It is difficult and challenging to study the dynamic behavior of Hadamard fractional differential equations. This manuscript mainly deals with the boundary value problem (BVP) of a nonlinear coupled Hadamard fractional system involving fractional derivative impulses. By applying nonlinear alternative of Leray-Schauder, we find some new conditions for the existence of solutions to this nonlinear coupled Hadamard fractional system. Our findings reveal that the impulsive function and its impulsive point have a great influence on the existence of the solution. As an application, we discuss an interesting example to verify the correctness and validity of our results.</p></abstract>

Almost Sure Exponential Stability of Uncertain Stochastic Hopfield Neural Networks Based on Subadditive Measures

“…Overall, this paper provides a valuable contribution to the field of neural networks by considering the effects of both stochastic and uncertain elements on network stability and proposing methods for analyzing such systems. This work can also extend to the two-layer cellular neural network,impulsive model, or the reaction diffusion model, as in Refs [30][31][32]. There is currently no corresponding research result for neural networks using uncertain stochastic neuron activation functions, uncertain stochastic two-layer cellular neural network, the uncertain stochastic impulsive model, or the reaction diffusion model, and researchers can develop these areas in the near future.…”

Coincidence Theory of a Nonlinear Periodic Sturm–Liouville System and Its Applications

“…Based on this paper, we will further continue to study the dynamics of Equation (1) under pulse, delay and random effects. In addition, inspired by the papers [13][14][15][16][17][18][19][20][22][23][24][42][43][44][45][46][47][48][49][50][51][52], we will also study the Sturm-Liouville equation involving fractional differential as well as reaction-diffusion terms in the future.…”

Stability and Numerical Simulation of a Nonlinear Hadamard Fractional Coupling Laplacian System with Symmetric Periodic Boundary Conditions

“…For more details on Hadamard fractional calculus, we refer the reader to [2][3][4][5][6] and the references therein. In recent years, the study of Hadamard fractional differential equations has attracted the attention of many scholars, mainly focusing on the existence, stability and approximation of solutions (see [7][8][9][10][11][12][13][14][15][16][17][18][19]). For example, Huang et al [9] applied a nonlinear alternative of Leray-Schauder to study the existence of solutions to a nonlinear coupled Hadamard fractional system.…”