TY - JOUR AU - Agarwal, R. P. AU - Hristova, S. AU - O'Regan, Donal PY - 2018 TI - Lyapunov functions to Caputo reaction-diffusion fractional neural networks with time-varying delays JO - Journal of Mathematics and Computer Science SP - 328--345 VL - 18 IS - 3 AB - A reaction diffusion equation with a Caputo fractional derivative in time and with time-varying delays is considered. Stability properties of the solutions are studied via the direct Lyapunov method and arbitrary Lyapunov functions (usually quadratic Lyapunov functions are used). In this paper we give a brief overview of the most popular fractional order derivatives of Lyapunov functions among Caputo fractional delay differential equations. These derivatives are applied to various types of reaction-diffusion fractional neural network with variable coefficients and time-varying delays. We show the quadratic Lyapunov functions and their Caputo fractional derivatives are not applicable in some cases when one studies stability properties. Some sufficient conditions for stability are obtained and we illustrate our theory on a particular nonlinear Caputo reaction-diffusion fractional neural network with time dependent delays. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.018.03.08 DO - 10.22436/jmcs.018.03.08 ID - Agarwal2018 ER - TY - JOUR TI - Lyapunov functions and strict stability of Caputo fractional differential equations AU - R. Agarwal AU - S. Hristova AU - D. O’Regan JO - Adv. Difference Equ. PY - 2015 DA - 2015// VL - 2015 ID - Agarwal2015 ER - TY - JOUR TI - Lyapunov functions and stability of Caputo fractional differential equations with delays AU - R. Agarwal AU - S. Hristova AU - D. 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