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• The work done in this paper provides the solutions for power access to rural and remote areas in developing nations. • The proposed affordable solution offers many advantages over the traditional central inverters. It provides more output power as compared to traditional central inverters under shading and dusting conditions. The results are validated through experimental investigation with regard to Indian weather conditions. • The proposed solution presents an optimal sizing strategy for Economically Weaker Section (EWS) for the low power rural household application. In literature, this kind of solution is yet not reported which makes this work novel. • This work presents the customized design of solar microinverter based PV System for different power provisioning levels for rural EWS houses. The proposed solution has an added advantage of addition of load in future without change in existing infrastructure. Reliable power supply is the key requirement for developing nations. Most of these nations are trying to modernize the rural lives by electrification in remote areas. Access to electricity is a bare requirement in future ages. This paper discusses the challenges faced by the utility companies in ensuring sustained electricity access to the new consumers followed by the various solutions. The techno – economic aspects of the proposed solution is validated by the experimental study. Based on the results, an optimal low-cost design is proposed in order for everyone to fulfil the minimum power needs. The paper presents an optimal size strategy for Economically Weaker Section (EWS) for the low power rural household application. The solar microinverter based PV System has been designed based on the daily load needs for one of the proposed layout plans of the (Gramin) Pradhan Mantri Awas Yojna adopted by Government of India. The proposed designs are also applicable for other developing nations. The proposed micro-inverter has been tested under different operating conditions and experimental validation proves its superiority over other inverter types, particularly for a low power application, as is the case for a typical low-income rural household. Economic considerations such as payback period has also been evaluated in this study. In addition, the proposed microinverter technology has also been tested in terms of power quality parameters under various operating conditions. [ABSTRACT FROM AUTHOR]

Edge theoretic extended contractions are introduced and coincidence point theorems and common fixed-point theorems are proved for such contraction mappings in a metric space endowed with a graph. As further applications, we have proved the existence of a solution of a nonlinear integral equation of Volterra type and given a suitable example in support of our result. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the (𝒞 , Ψ * , G) class of contraction mappings using C-class functions and some improved control functions for a pair of set valued mappings as well as a pair of single-valued mappings, and prove common fixed point theorems for such mappings in a metric space endowed with a graph. Our results unify and generalize many important fixed point results existing in literature. As an application of our main result, we have derived fixed point theorems for a pair of α -admissible set valued mappings in a metric space. [ABSTRACT FROM AUTHOR]