Hemant Kumar Nashine

Bio: Hemant Kumar Nashine is an academic researcher from VIT University. The author has contributed to research in topics: Fixed-point theorem & Metric space. The author has an hindex of 1, co-authored 9 publications receiving 8 citations.

Identification of source term for the ill-posed Rayleigh–Stokes problem by Tikhonov regularization method

Abstract: In this paper, we study an inverse source problem for the Rayleigh–Stokes problem for a generalized second-grade fluid with a fractional derivative model. The problem is severely ill-posed in the sense of Hadamard. To regularize the unstable solution, we apply the Tikhonov method regularization solution and obtain an a priori error estimate between the exact solution and regularized solutions. We also propose methods for both a priori and a posteriori parameter choice rules. In addition, we verify the proposed regularized methods by numerical experiments to estimate the errors between the regularized and exact solutions.

Wardowski-Feng-Liu type fixed point theorems for multivalued mappings

Abstract: In this work, we present some Wardowski-Feng-Liu type fixed point theorems for multivalued mappings in complete (ordered) metric spaces. The obtained results generalize and improve several existing theorems in the literature. The given notions and outcome are illustrated by an appropriate example. An application to existence of solutions for Fredholm-type integral inclusions is presented.

Solvability of a fractional Cauchy problem based on modified fixed point results of non-compactness measures

Abstract: We study the solvability of a fractional Cauchy problem based on new development of fixed point theorem, where the operator is suggested to be non-compact on its domain. Moreover, we shall prove that the solution is bounded by a fractional entropy (entropy solution). For this purpose, we establish a collection of basic fixed point results, which generalizes and modifies some well known results. Our attention is toward the concept of a measure of non-compactness to generalize $\mu$-set contractive condition, using three control functions.

Solution of a fractal energy integral operator without body force using measure of noncompactness

Abstract: In this paper, we study the solution of fractal energy integral equation for one-dimensional compressible flows without body force using measure of noncompactness. We also discuss the solution of the local fractal equation of losing energy system using the notion of local fractal differential idea. For this, a new notion of χ - Δ -set contraction condition under simulation function is defined and two main fixed point and coupled fixed point results are obtained.

Fixed Points for Multivalued Mappings and the Metric Completeness = จุดตรึงสำหรับการส่งหลายค่าและความบริบูรณ์เชิงเมตริก / Hatairat Yingtaweesittikul

Abstract: We consider the equivalence of the existence of fixed points of single-valued mappings and multivalued mappings for some classes of mappings by proving some equivalence theorems for the completeness of metric spaces.

The Existence of Solutions to Nonlinear Matrix Equations via Fixed Points of Multivalued F-Contractions

Abstract: In this paper, we set up an adequate condition for the presence of a solution of the nonlinear matrix equation. To do so, we prove the existence of fixed points for multi-valued modified F-contractions in the context of complete metric spaces, which generalize, refine, and extend several existing results in the literature. An example is accompanies the obtained results to show that derived results are a proper generalization.

The analytical analysis of nonlinear fractional-order dynamical models

Abstract: The present research paper is related to the analytical solution of fractional-order nonlinear Swift-Hohenberg equations using an efficient technique. The presented model is related to the temperature and thermal convection of fluid dynamics which can also be used to explain the formation process in liquid surfaces bounded along a horizontally well-conducting boundary. In this work Laplace Adomian decomposition method is implemented because it require small volume of calculations. Unlike the variational iteration method and Homotopy pertubation method, the suggested technique required no variational parameter and having simple calculation of fractional derivative respectively. Numerical examples verify the validity of the suggested method. It is confirmed that the present method's solutions are in close contact with the solutions of other existing methods. It is also investigated through graphs and tables that the suggested method's solutions are almost identical with different analytical methods.

On F-Contractions: A Survey

Abstract: D. Wardowski proved in 2012 a generalization of Banach Contraction Principle by introducing F-contractions in metric spaces. In the next ten years, a great number of researchers used Wardowski's approach, or some of its modifications, to obtain new fixed point results for single- and multivalued mappings in various kinds of spaces. In this review article, we present a survey of these investigations, including some improvements, in particular concerning conditions imposed on function F entering the contractive condition.

Use of Neural Network Based Prediction Algorithms for Powering Up Smart Portable Accessories

Abstract: Emerging Trends in the use of smart portable accessories, particularly within the context of the Internet of Things (IoT), where smart sensor devices are employed for data gathering, require advancements in energy management mechanisms. This study aims to provide an intelligent energy management mechanism for wearable/portable devices through the use of predictions, monitoring, and analysis of the performance indicators for energy harvesting, majorly focusing on the hybrid PV-wind systems. To design a robust and precise model, prediction algorithms are compared and analysed for an efficient decision support system. Levenberg–Marquardt (LM), Bayesian Regularization (BR), and Scaled Conjugate Gradient (SCG) prediction algorithms are used to develop a Shallow Neural Network (SNN) for time series prediction. The proposed SNN model uses a closed-loop NARX recurrent dynamic neural network to predict the active power and energy of a hybrid system based on the experimental data of solar irradiation, wind speed, wind direction, humidity, precipitation, ambient temperature and atmospheric pressure collected from Jan 1st 2015 to Dec 26th 2015. The historical hourly metrological data set is established using calibrated sensors deployed at Middle East Technical University (METU), NCC. The accessory considered in this study is called as Smart Umbrella System (SUS), which uses a Raspberry Pi module to fetch the weather data from the current location and store it in the cloud to be processed using SNN classified prediction algorithms. The results obtained show that using the SNN model, it is possible to obtain predictions with 0.004 error rate in a computationally efficient way within 20 s. With the experiments, we are able to observe that for the period of observation, the energy harvested is 178 Wh/d, where the system estimates energy as 176.5 Wh/d, powering the portable accessories accurately.