Smart mobile devices are being widely used to identify and track human behaviors in simple and complex daily activities. The evolution of wearable sensing technologies pertaining to wellness, living surveillance, and fitness tracking is based on the accurate analysis of people’s behavior from the data acquired through different sensors embedded in smart devices, especially wrist-worn wearable technologies such as smartwatches. Many deep learning techniques have been developed to realize human activity recognition (HAR), with simple daily activities being focused on. However, several challenges remain to be addressed in complex HAR research involving specific human behaviors in different contexts. To address the problems pertaining to complex HAR, a deep neural network composed of convolutional layers and residual networks was developed in this work. Additional attention was incorporated in the system by using a squeeze-and-excite mechanism. The model effectiveness was investigated considering three publicly available datasets, (WISDM-HARB, UT-Smoke, and UT-Complex). The proposed network achieved overall accuracies of 94.91%, 98.75%, and 97.73% over WISDM-HARB, UT-Smoke, and UT-Complex, respectively. The results showed that deep residual networks are more durable and superior at activity recognition than the existing models.

This paper presents a class of implicit pantograph fractional differential equation with more general Riemann-Liouville fractional integral condition. A certain class of generalized fractional derivative is used to set the problem. The existence and uniqueness of the problem is obtained using Schaefer’s and Banach fixed point theorems. In addition, the Ulam-Hyers and generalized Ulam-Hyers stability of the problem are established. Finally, some examples are given to illustrative the results.

One of the fastest growing and efficient methods for solving the unconstrained minimization problem is the conjugate gradient method (CG). Recently, considerable efforts have been made to extend the CG method for solving monotone nonlinear equations. In this research article, we present a modification of the Fletcher–Reeves (FR) conjugate gradient projection method for constrained monotone nonlinear equations. The method possesses sufficient descent property and its global convergence was proved using some appropriate assumptions. Two sets of numerical experiments were carried out to show the good performance of the proposed method compared with some existing ones. The first experiment was for solving monotone constrained nonlinear equations using some benchmark test problem while the second experiment was applying the method in signal and image recovery problems arising from compressive sensing.

In this paper, we study and investigate an interesting Caputo fractional derivative and Riemann–Liouville integral boundary value problem (BVP): ^c $D_{0^{+}}^{q}u\left(t\right)=f(t,u\left(t\right)),t\in [0,T]$ , ${\displaystyle u^{\left(k\right)}\left(0\right)={\xi }_k,u\left(T\right)=\sum _{i=1}^m{{\beta }_i}_{RL}{I}_{0^{+}}^{p_i}u\left({\eta }_i\right),}$ where $n-1<q<n,n\ge 2,m,n\in \mathbb{N}$ , ${\xi }_k,{\beta }_i\in \mathbb{R}$ , $k=0,1,\dots ,n-2$ , $i=1,2,\dots ,m$ , and ^c $D_{0^{+}}^q$ is the Caputo fractional derivatives, $f:[0,T]\times C\left(\right[0,T],E)\to E$ , where E is the Banach space. The space E is chosen as an arbitrary Banach space; it can also be $\mathbb{R}$ (with the absolute value) or $C\left(\right[0,T],\mathbb{R})$ with the supremum-norm. _RL $I_{0^{+}}^{p_i}$ is the Riemann–Liouville fractional integral of order $p_i>0$ , ${\eta }_i\in (0,T)$ , and ${\displaystyle \sum _{i=1}^m{\beta }_i{\eta }_i^{p_i+n-1}\frac{\Gamma \left(n\right)}{\Gamma (n+p_i)}\ne T^{n-1}}$ . Via the fixed point theorems of Krasnoselskii and Darbo, the authors study the existence of solutions to this problem. An example is included to illustrate the applicability of their results.

In this modern era, nanofluids are considered one of the advanced kinds of heat transferring fluids due to their enhanced thermal features. The present study is conducted to investigate that how the suspension of molybdenum-disulfide $\left(Mo{S}_2\right)$ nanoparticles boosts the thermal performance of a Casson-type fluid. Sodium alginate (NaAlg) based nanofluid is contained inside a vertical channel of width d and it exhibits a flow due to the movement of the left wall. The walls are nested in a permeable medium, and a uniform magnetic field and radiation flux are also involved in determining flow patterns and thermal behavior of the nanofluid. Depending on velocity boundary conditions, the flow phenomenon is examined for three different situations. To evaluate the influence of shape factor, $Mo{S}_2$ nanoparticles of blade, cylinder, platelet, and brick shapes are considered. The mathematical modeling is performed in the form of non-integer order operators, and a double fractional analysis is carried out by separately solving Caputo-Fabrizio and Atangana-Baleanu operators based fractional models. The system of coupled PDEs is converted to ODEs by operating the Laplace transformation, and Zakian’s algorithm is applied to approximate the Laplace inversion numerically. The solutions of flow and energy equations are presented in terms of graphical illustrations and tables to discuss important physical aspects of the observed problem. Moreover, a detailed inspection on shear stress and Nusselt number is carried out to get a deep insight into skin friction and heat transfer mechanisms. It is analyzed that the suspension of $Mo{S}_2$ nanoparticles leads to ameliorating the heat transfer rate up to 9.5%. To serve the purpose of achieving maximum heat transfer rate and reduced skin friction, the Atangana-Baleanu operator based fractional model is more effective. Furthermore, it is perceived that velocity and energy functions of the nanofluid exhibit significant variations because of the different shapes of nanoparticles.