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Salt stress is the major risk to the seed germination and plant growth via affecting physiological and biochemical activities in plants. Zinc nanoparticles (ZnNPs) are emerged as a key agent in regulating the tolerance mechanism in plants under environmental stresses. However, the tolerance mechanisms which are regulated by ZnNPs in plants are still not fully understood. Therefore, the observation was planned to explore the role of ZnNPs (applied as priming and foliar) in reducing the harmful influence of sodium chloride (NaCl) stress on the development of spinach (Spinacia oleracea L.) plants. Varying concentrations of ZnNPs (0.1%, 0.2% & 0.3%) were employed to the spinach as seed priming and foliar, under control as well as salt stress environment. The alleviation of stress was observed in ZnNPs-applied spinach plants grown under salt stress, with a reduced rise in the concentration hydrogen peroxide, melondialdehyde and anthocyanin contents. A clear decline in soluble proteins, chlorophyll contents, ascorbic acid, sugars, and total phenolic contents was observed in stressed conditions. Exogenous ZnNPs suppressed the NaCl generated reduction in biochemical traits, and progress of spinach plants. However, ZnNPs spray at 0.3% followed by priming was the most prominent treatment in the accumulation of osmolytes and the production of antioxidant molecules in plants.

In this paper, Petrović’s inequality is generalized for \(h−\)convex functions on coordinates with the condition that \(h\) is supermultiplicative. In the case, when \(h\) is submultiplicative, Petrović’s inequality is generalized for \(h−\) concave functions. Also particular cases for \(P−\) function, Godunova-Levin functions, \(s−\) Godunova-Levin functions and \(s−\) convex functions has been discussed.

The escalating energy demand across the globe has intensified the electricity production. Owing to the unavailability of the reliable techniques for electricity storage for a long duration, it is consumed immediately after its production. Therefore, electricity markets can’t be handled like the conventional stock markets. Power companies are facing immense price and delivery risks owing to the increasing competition in the electricity markets. As a result, risk management is the fundamental concern to be addressed in order to achieve the optimum profit targets. Consequently, the power generation organizations need to allocate their generation in bilateral contracts and spot market. For this purpose, an optimal theory of portfolio selection is proposed in this study for electricity generation by forming a reliable prototype and applying the proposed scheme to obtain the suitable outcomes. The Paris Accord on environmental safety from carbon dioxide and NOx gases is especially considered during the modeling of the proposed technique. The credibility of the proposed scheme is validated by using the real-time market data from the PJM market. Various risk-return tradeoffs are implemented, and their corresponding solutions are acquired for portfolio optimization as corroborated by the results. The suggested technique is found reliable and adequate for the carbon tax paying suppliers around the world for allocating their respective generation based on the demand of the consumers.

The k-fractional integrals introduced by S. Mubeen and G. M. Habibullah in 2012 are a generalization of Riemann–Liouville fractional integrals. Some estimations of these fractional integrals via convexity have been established.

The study of integral operators has always been important in the subjects of mathematics, physics, and in diverse areas of applied sciences. It has been challenging to discover and formulate new types of integral operators. The aim of this paper is to study and formulate an integral operator of a general nature. Under some suitable conditions the existence of a new integral operator is established. The boundedness of left and right sided integral operators is obtained and further boundedness of their sum is given. The investigated integral operators derive several known integrals and have interesting consequences for fractional calculus integral operators and conformable integrals. The presented results provide the boundedness of various fractional and conformable integral operators simultaneously.

The study underhand is aimed to estimate the impact of socioeconomic characteristics of school teachers on their job performance. The data were collected by using well-structured and pre-tested questionnaire. A sample of 200 respondents from ESTs elementary school female teachers were selected through simple random sampling technique from tehsil Vehari. Descriptive statistics i.e. frequency, percentage and mean values were used to analyze the data. The results showed that the teacher performance was depending on many factors i.e. free accommodation, weekly duty allowances, advance payment from the school in case of financial problem, provision of prizes, provision of free medical care and a satisfactory standard of living. The result also showed that the salary and financial benefits have high impact on teachers’ performance. The results also found significant impact of socioeconomic characteristics on teacher’s performance

In this paper certain Polya-Szego type integral inequalities due to Karamata's estimations of the Chebyshev quotient are presented. Those inequalities include an extended generalized Mittag-Leffler function with the corresponding fractional integral operator, and from them, some fractional integral inequalities of Chebyshev type are obtained. Also, several known results are improved.

This paper studies the $k$ -fractional analogue of the Caputo fractional derivatives, their properties, and applications. A convolution of two functions instead of the product is analyzed by means of Caputo $k$ -fractional derivatives. By virtue of defined convolution Chebyshev type, inequalities have been investigated. Moreover, Hadamard Caputo fractional inequalities have been estimated by using definition of quasi-convex functions.

In this paper we are presenting the refinements of integral inequalities established for convex functions. Consequently, we get refinements of several fractional integral inequalities for different kinds of fractional integral operators.

This paper deals with generalized integral operator inequalities which are established by using φ -quasiconvex functions. Bounds of an integral operator are established which have connections with different kinds of known fractional integral operators. All the results are deducible for quasiconvex functions. Some fractional integral inequalities are deduced.

In this paper, two versions of the Hadamard inequality are obtained by using Caputo fractional derivatives and stronglym-convex functions. The established results will provide refinements of well-known Caputo fractional derivative Hadamard inequalities form-convex and convex functions. Also, error estimations of Caputo fractional derivative Hadamard inequalities are proved and show that these are better than error estimations already existing in literature.

The main aim of this paper is to give refinement of bounds of fractional integral operators involving extended generalized Mittag-Leffler functions. A new definition, namely, strongly α,m-convex function is introduced to obtain improvements of bounds of fractional integral operators for convex, m-convex, and α,m-convex functions. The results of this paper will provide simultaneous generalizations as well as refinements of various published results.

In today’s technological world, confidentiality is an important issue to deal with, and it is carried out through different proficiencies. Cryptography is a scientific technique of securing a communication from unauthenticated approach. There exist many encryption algorithms in cryptography for data security. The need of new nonstandard encryption algorithms has been raised to prevent the communication from traditional attacks. This paper proposes some new encryption algorithms for secure transmission of messages using some special corona graphs and bipartite graph along with some algebraic properties. These proposed encryption schemes will lead to more secure communication of secret messages.

In this paper, we define a strongly exponentially α , h − m -convex function that generates several kinds of strongly convex and convex functions. The left and right unified integral operators of these functions satisfy some integral inequalities which are directly related to many unified and fractional integral inequalities. From the results of this paper, one can obtain various fractional integral operator inequalities that already exist in the literature.

In this paper, we present two versions of the Hadamard inequality forα,mconvex functions via Caputo fractional derivatives. Several related results are analyzed for convex andm-convex functions along with their refinements and generalizations. The error bounds of the Hadamard inequalities are established by applying some known identities.

In this article, we have established the Hadamard inequalities for strongly convex functions using generalized Riemann–Liouville fractional integrals. The findings of this paper provide refinements of some fractional integral inequalities. Furthermore, the error bounds of these inequalities are given by using two generalized integral identities.

In this paper, we introduce α,h−m−p-convex function and some related functions. By applying this generalized definition, new versions of Hadamard and Fejér–Hadamard fractional integral inequalities for Riemann–Liouville fractional integrals are given. The presented results hold at the same time for different types of convexities.

Zigzag silicon nanowires (SiNWs) attract great interest due to their unique physical/chemical properties that make them appealing in various applications; yet, their fabrication has always been difficult and the formation mechanism for zigzag silicon nanostructures remains elusive. In this work, the influence of temperature on the morpholohies of SiNWs by metal-assisted chemical etching (MatEtch or MACE) in aqueous HF-H2O2-C3H8O3 solution is systematically analyzed. It is found that zigzag-shaped silicon nanowires can be fabricated through a slow etching process at low temperatures in the presence of glycerol (C3H8O3). The synergistic effect of glycerol and low etchant-temperatures varied from 15 °C to 35 °C facilitate the fabrication of zigzag-SiNWs. The arm length of the zigzag design increases with the increase of temperature. However, straight SiNWs are fabricated at higher temperatures, such as those greater than 35 °C. It is also shown that for dispersed AgNPs, straight channels can be obtained at higher temperatures, while low temperature favors zigzag channels with decreasing arm length. We anticipate that these findings provide scientific guidance for the controlled fabrication of large-scale zigzag SiNW arrays.

Cotton is an important fiber and cash crop. Extreme water scarceness affects the growth, quality, and productivity of cotton. Water shortage has threatened the future scenario for cotton growers, so it is imperative to devise a solution to this problem. In this research, we have tried to machinate a solution for it. 23 genotypes have been screened out against drought tolerance at the seedling stage by evaluating the morphological, physiological, and biochemical traits in a triplicate completely randomized design plot experiment with two water regimes [50 and 100% field capacity]. Genotypic differences for all the morphological and physiological traits revealed highly significant differences except transpiration rate (TR). Moreover, the interaction between genotype and water regime (G × W) was highly significant for root length (RL, 5.163), shoot length (SL, 11.751), excised leaf water loss (ELWL, 0.041), and stomatal conductance (SC, 7.406). A positively strong correlation was found in TR with relative water content (RWC; 0.510) and SC (0.584) and RWC with photosynthesis (0.452) under drought conditions. A negative correlation was found in SC with SL (−0.428) and photosynthesis (−0.446). Traits like RL, SL, SC, photosynthesis, proline, catalase, and malondialdehyde were visible indicators, which can differentiate drought-tolerant genotypes from the susceptible ones. A wide range of diversity was found in all the morpho-physiological traits with the cumulative variance of four principal components (PCs) 83.09% and three PCs 73.41% under normal and water-stressed conditions, respectively, as per the principal component analysis. Hence, selection criteria can be established on the aforementioned traits for the development of drought-tolerant cultivars. Moreover, it was found that out of 23 experimental varieties, NIAB-135, NIAB-512, and CIM-554 could be used to devise breeding strategies for improving drought tolerance in cotton.

The aim of this paper is to generalize the fractional Hadamard and Fejér–Hadamard inequalities. By using a generalized fractional integral operator containing extended Mittag-Leffler function via monotone function, for convex functions we generalize well known fractional Hadamard and Fejér–Hadamard inequalities. Also we study the error bounds of these generalized Hadamard and Fejér–Hadamard inequalities. We also obtain some published results from presented inequalities.

The aim of this paper is to establish new generalized fractional versions of the Hadamard and the Fejér–Hadamard integral inequalities for harmonically convex functions. Fractional integral operators involving an extended generalized Mittag-Leffler function which are further generalized via a monotone increasing function are utilized to get these generalized fractional versions. The results of this paper give several consequent fractional inequalities for harmonically convex functions for known fractional integral operators deducible from utilized generalized fractional integral operators.

Nitric oxide (NO) is a key signaling molecule that instigates significant changes in plant metabolic processes and promotes tolerance against various environmental stresses including drought. In this study, we focused on NO-mediated physiological mechanisms and enzymatic activities that influence the nutrient concentrations and yield in maize under drought stress. The drought-tolerant (NK-8711) and sensitive (P-1574) maize hybrids were sown in lysimeter tanks and two levels of water stress (well-watered at100% field capacity and drought stress at 60% field capacity) were applied at three-leaves stage of maize. Foliar treatment of sodium nitroprusside (SNP), the donor of NO was applied at the cob development stage. The results showed that the foliar spray of NO regulated water relations by increasing proline content and improved drought tolerance in water stressed maize plants. In addition, it stimulated the activity of antioxidative enzymes which reduced the production of free radicals and lipid peroxidation. The activities of nitrate assimilation enzymes were considerably increased by NO spray which, in turn, increased nutrient accumulation and yield in maize under water deficit conditions. These results acknowledge the importance of NO as a stress-signaling molecule that positively regulates defense mechanisms in maize to withstand water-limited conditions.

The developed world is experiencing a rapid change in terms of technology due to Artificial Intelligence, Deep Learning, and the Internet of Things. However, in the developing countries, the industry devices are operated on manual control, therefore industries required fmances and men’s power to manage electronic machines. This work aims to provide automated control to the industry devices by developing an Embedded System (ES) that is further coupled with a personal computer (PC) to regulate the status of devices. The status (OFF/ON) of the devices can be seen on the web browser. Moreover, we have developed a Graphical User Interface (GUI) is in HTML to see the status of devices online. The GUI is equipped with a secure mechanism by including a separate login page and password to access the control. It ensures that only authorized individuals can access and monitor the status of connected devices. The proposed architecture is capable of providing ease to the offices, industry and homes by providing remote access to the system. Additionally, the GUI can be opened on smartphones, laptops, tablets due to autonomous control. The proposed system is energy-efficient, robust, and affordable as compared to the existing automation systems.

This work deals with the bounds of a unified integral operator with which several fractional and conformable integral operators are directly associated. By using quasiconvex and monotone functions we establish bounds of these integral operators. We prove their boundedness and continuity. The results of this paper generalize already published results and have direct consequences for fractional and conformable integrals

The main objective of this paper is to obtain the fractional integral operator inequalities which provide bounds of the sum of these operators at an arbitrary point. These inequalities are derived for s-exponentially convex functions. Furthermore, a Hadamard inequality is obtained for fractional integrals by using exponentially symmetric functions. The results of this paper contain several such consequences for known fractional integrals and functions which are convex, exponentially convex, and s-convex.

In this paper, we define a new function, namely, harmonically α , h − m -convex function, which unifies various kinds of harmonically convex functions. Generalized versions of the Hadamard and the Fejér–Hadamard fractional integral inequalities for harmonically α , h − m -convex functions via generalized fractional integral operators are proved. From presented results, a series of fractional integral inequalities can be obtained for harmonically convex, harmonically h − m -convex, harmonically α , m -convex, and related functions and for already known fractional integral operators.

In this paper, we are interested to deal with unified integral operators for strongly φ -convex function. We will present refinements of bounds of these unified integral operators and use them to get associated results for fractional integral operators. Several known results are connected with particular assumptions.

Nanocrystalline Ni-Zn ferrite nanoparticles (NPs) NixZn1−xFe2O4 have been synthesized followed by detailed analysis of compositional effects on morphology, crystalline phase formation, lattice constant, crystallite size, magnetic, optical and dielectric properties describing the underlying physics as well. Cubic spinel structure with (311) preferred orientation and switching trend in crystallite size variation with gradual decrease in lattice parameter (from 8.377 to 8.323 A) with the increase in nickel content has been observed through calculations. The magnetic behavior of NPs has been investigated at lower temperatures up to 5 K illustrating significantly improved magnetic parameters including Ms = 36.8 emu/g, Mr = 3.61 emu/g, SQ = Mr/Ms = 0.1028, Hc = 115.33 Oe, μB = 1.5664 emu, and K1 = 2122.18 erg/g. This enhancement has been found possibly due to less thermal fluctuations and significant superparamagnetic contributions from the very small fine nanoparticles being in blocking state owing to such a cool environment. Optical band gap for both direct (1.74–1.39 eV) and indirect (1.25–1.16 eV) transitions shows decreasing trend with the increase in Ni contents probably due to the redistribution of Ni or Zn contents from octahedral to tetrahedral site. Dielectric constant (real and imaginary) and tangent loss decreased with the increase of frequency, this refers to the Maxwell-Wagner type of polarization in the material in accordance with Koop’s theory, however, a switching is observed at the stoichiometric ratio of x = 0.25 and 0.75. The impedance (Z′) has maximum value 5539 kΩ at x = 0.75 and a minimum value 682 kΩ at x = 1.0. The Nyquist plot pointed out the contribution of grain boundaries, however the contribution varies with the stoichiometric ratio x. The Cole-Cole plot confirms the contribution of grains in the material for all value of x.

In this paper we generalize some Riemann-Liouville fractional integral inequalities of Ostrowski type for h-convex functions via Katugampola fractional integrals, generalization of Riemann- Liouville and the Hadamard fractional integrals. Also we deduce some known results by using p-functions, convex functions and s-convex functions.

In this work, the influence of external magnetic field on the laser-induced breakdown spectroscopy of laser-induced plasma as a function of pressures has been examined. Aluminum samples are analyzed by using Nd:YAG (1064 nm, 8 ns) under helium and argon gases at pressure ranging from 1 to 80 kPa. It is revealed that spectral intensity and plasma parameters are significantly influenced by the presence of magnetic field and ambient gas condition as well. In the presence of magnetic field, emitted intensity of various atomic and ionic lines (384.8 nm, 386.8 nm, 410.4 nm) is found to be higher at various ambient gas pressures. The stark broadening analysis confirms that the values of electron density are increased by the magnetic field at different pressures and distances.

In this paper we give generalizations of the Hadamard-type inequalities for fractional integrals. As special cases we derive several Hadamard type inequalities.

We are pleased to investigate some Riemann–Liouville fractional integral inequalities in a very simple and novel way. By using convexity of a function f and a simple inequality over the domain of f we establish some interesting results.

Parametric uncertainties and coupled nonlinear dynamics are inherent in quadrotor configuration and infer adaptive nonlinear approaches to be used for flight control system. Numerous adapt...

In this paper we are interested to present some general fractional integral inequalities for m-convex functions by involving generalized Mittag-Leffler function. In particular we produce inequalities for several kinds of fractional integrals. Also these inequalities have some connections with known integral inequalities.

Integral operators of a fractional order containing the Mittag-Leffler function are important generalizations of classical Riemann–Liouville integrals. The inequalities that are extensively studied for fractional integral operators are the Hadamard type inequalities. The aim of this paper is to find new versions of the Fejér–Hadamard (weighted version of the Hadamard inequality) type inequalities for (α, h-m)-p-convex functions via extended generalized fractional integrals containing Mittag-Leffler functions. These inequalities hold simultaneously for different types of well-known convexities as well as for different kinds of fractional integrals. Hence, the presented results provide more generalized forms of the Hadamard type inequalities as compared to the inequalities that already exist in the literature.

In this paper, we give some fractional integral inequalities of Ostrowski type for s-Godunova-Levin functions via Katugampola fractional integrals. We also deduce some known Ostrowski type fractional integral inequalities for Riemann-Liouville fractional integrals.

The aim of this paper is to obtain some more general fractional integral inequalities of Fejer Hadamard type for p-convex functions via Riemann-Liouville k-fractional integrals. Also in particular fractional inequalities for p-convex functions via Riemann-Liouville fractional integrals have been deduced.

In this paper we prove Hadamard-type inequalities for m-convex function via Riemann-Liouville fractional integrals and Hadamard-type in- equalities for convex function via Riemann-Liouville fractional integral are deduced. Also we find connection with some well known results related to Hadamard inequality.

In this paper we are interested to present the Hadamard and the Fejer–Hadamard type integral inequalities for harmonically convex functions via two sided generalized fractional integral operator. Presented results have connection with some known results about the Hadamard and the Fejer–Hadamard type inequalities for two sided Riemann–Liouville fractional integral operator.

Fractional inequalities are useful in establishing the uniqueness of solution for partial differential equations of fractional order. Also they provide upper and lower bounds for solutions of fractional boundary value problems. In this paper we obtain some general integral inequalities containing generalized Mittag-Leffler function and some already known integral inequalities have been produced as special cases.

This research explores Caputo k-fractional integral inequalities for functions whose nth order derivatives are absolutely continuous and possess Grüss type variable bounds. Using Chebyshev inequality (Waheed et al. in IEEE Access 7:32137–32145, 2019) for Caputo k-fractional derivatives, several integral inequalities are derived. Further, Laplace transform of Caputo k-fractional derivative is presented and Caputo k-fractional derivative and Riemann–Liouville k-fractional integral of an extended generalized Mittag-Leffler function are calculated. Moreover, using the extended generalized Mittag-Leffler function, Caputo k-fractional differential equations are presented and their solutions are proposed by applying the Laplace transform technique.

This paper is dedicated to Opial-type inequalities for arbitrary kernels using convex functions. These inequalities are further applied to a power function. Applications of the presented results are studied in fractional calculus via fractional integral operators by associating special kernels.