The summation inequality is essential in creating delay-dependent criteria for discrete-time systems with time-varying delays and developing other delay-dependent standards. This paper uses our rebuilt summation inequality to investigate the robust stability analysis issue for discrete-time neural networks that incorporate interval time-varying leakage and discrete and distributed delays. It is a novelty of this study to consider a new inequality, which makes it less conservative than the well-known Jensen inequality, and use it in the context of discrete-time delay systems. Further stability and passivity criteria are obtained in terms of linear matrix inequalities (LMIs) using the Lyapunov-Krasovskii stability theory, coefficient matrix decomposition technique, mobilization of zero equation, mixed model transformation, and reciprocally convex combination. With the assistance of the LMI Control toolbox in Matlab, numerical examples are provided to demonstrate the validity and efficiency of the theoretical findings of this research.

A vital role of ternary hybrid nanofluid is visualized as a significant improvement of thermal performance and enhancement in thermal rate which is applicable in automobiles for coolant process, thermodynamics of fuel. This process of ternary hybrid nanofluid is utilized to enhance maximum performance of thermal energy and applicable in chemical products, solar power, melting process, wire paintings, biological products, solar system, cooling process, glasses melting, glass fiber, metal grinding etc. Three-dimensional motion of ternary hybrid nanoparticles in partially Casson fluid over a vertical stretching surface is addressed using Darcy's Forchheirmer theory. Further, effects of Joule heating, non-uniform thermal radiation and viscous dissipation are considered in the energy equation and motion of ethylene glycol contains alumina, silica, and titania nanoparticles with various shape effects. Similarity variables are utilized to derive the system of ODEs from PDEs. A system of ODEs is numerically solved by a finite element method. It was concluded that the thermal field for platelet nanoparticles is greater than the thermal field for cylindrical nanoparticles. Nusselt number increases versus change in ion slip, Hall and magnetic parameters. Maximum production of heat energy is obtained for the case of tri-hybrid nanomaterial rather than for the case of hybrid nanomaterial.

This paper explicates the Razumikhin-type uniform stability and a uniform asymptotic stability theorem for the conformable fractional system with delay. Based on a Razumikhin-Lyapunov functional and some inequalities, a delay-dependent asymptotic stability criterion is in the term of a linear matrix inequality (LMI) for the conformable fractional linear system with delay. Moreover, an application of our theorem is illustrated via a numerical example.