Author

# Hemant Kumar Nashine

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

##### Papers

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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.

3 citations

01 Jan 2015

Abstract: In the present paper, we derive a common xed point theorem for a hybrid pair of occasionally coincidentally idempotent mappings satisfying closed multi-valued F -contraction condition introduced by Wardowski (Fixed Point Theory Appl. 2012:94) via common limit range property in the frame of complete metric spaces. Also, hybrid mappings which satisfy an F -contractive condition of Hardy-Rogers type are considered. Our results improve several results from the existing literature. Two applications are presented|the proofs of existence of solutions for certain system of functional equations arising in dynamic programming, as well as for certain Volterra integral inclusion.

1 citations

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24 Jun 2019

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.

1 citations

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1 citations

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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.

1 citations

##### Cited by

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01 Jan 2010

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.

50 citations

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07 Feb 2020

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.

5 citations

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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.

3 citations

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01 Jan 2021

Abstract: In this chapter, we use the concept of local fractional calculus and measure of non-compactness to design the growth system of Covid-19. To achieve this, we establish a fixed point and coupled fixed point theorems for new \(\mu \)-set contraction condition in partially ordered Banach spaces, whose positive cone \(\mathbb {K}\) is normal. We provide adequate examples to validate the epidemic dynamics with graphical presentations. We also use present available data to validate it.

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Abstract: The approximate controllability of second-order integro-differential evolution control systems using resolvent operators is the focus of this work. We analyze approximate controllability outcomes by referring to fractional theories, resolvent operators, semigroup theory, Gronwall’s inequality, and Lipschitz condition. The article avoids the use of well-known fixed point theorem approaches. We have also included one example of theoretical consequences that has been validated.