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The characterization of PV unit can be made using one-, two-, and triple-diode electrical model. Each model has its own merits in terms of number of unknown parameters to be extracted and burden of calculation, and etc. In most applications, one-diode model (1-DM) is sufficed for the purpose of simulation and analysis in steady-state and dynamic conditions. This paper cares of extracting the unknown five parameters of the 1-DM exploiting the real I-V dataset points. New effort of employing the slime mould algorithm (SMA) and its improved version (ImSMA) is addressed to attain the same goal. Lambert W-function or omega function is used for accurate calculus of PV current. Two benchmarking test cases widely used in the literature are demonstrated and analysed to appraise the performance of SMA/ImSMA complete with subsequent analysis and discussions. The best ImSMA’s results of root mean squared current errors are 7.73006e−4 A and 1.3798e−2 A for RTC solar cell and STP6-120/36; respectively. Various scenarios under varied conditions are demonstrated utilizing the cropped best values of the model’s parameters In addition to that, performance measures are made to validate the cropped results along with comparisons to other recent competing algorithms. It can be concluded that the validations in consort with established outcomes signify the ImSMA in recognizing the PV unidentified 1-DM parameters.

The scope of our investigation is to study the geometric properties of the normalized form of the combination of generalized Lommel–Wright function $J_{\nu ,\lambda }^{\mu ,m}$ J ν , λ μ , m defined by $\mathfrak{J}_{\nu ,\lambda }^{\mu ,m}(z):=\Gamma ^{m}(\lambda +1) \Gamma (\lambda +\nu +1)2^{2\lambda +\nu } z^{1-(\nu /2)-\lambda } \mathcal{I}_{\nu ,\lambda }^{\mu ,m}(\sqrt{z})$ J ν , λ μ , m ( z ) : = Γ m ( λ + 1 ) Γ ( λ + ν + 1 ) 2 2 λ + ν z 1 − ( ν / 2 ) − λ I ν , λ μ , m ( z ) , where $\mathcal{I}_{\nu ,\lambda }^{\mu ,m}(z):=(1-2\lambda -\nu )J_{\nu , \lambda }^{\mu ,m}(z)+z (J_{\nu ,\lambda }^{\mu ,m}(z) )^{ \prime }$ I ν , λ μ , m ( z ) : = ( 1 − 2 λ − ν ) J ν , λ μ , m ( z ) + z ( J ν , λ μ , m ( z ) ) ′ and $$ J_{\nu ,\lambda }^{\mu ,m}(z)= \biggl(\frac{z}{2} \biggr)^{2\lambda + \nu } \sum_{n=0}^{\infty } \frac{(-1)^{n}}{\Gamma ^{m} (n+\lambda +1 )\Gamma (n\mu +\nu +\lambda +1 )} \biggl(\frac{z}{2} \biggr)^{2n}, $$ J ν , λ μ , m ( z ) = ( z 2 ) 2 λ + ν ∑ n = 0 ∞ ( − 1 ) n Γ m ( n + λ + 1 ) Γ ( n μ + ν + λ + 1 ) ( z 2 ) 2 n , with $m\in \mathbb{N}$ m ∈ N , $\mu >0$ μ > 0 and $\lambda ,\nu \in \mathbb{C}$ λ , ν ∈ C , including starlikeness and convexity of order α ($0\leq \alpha 0 ≤ α < 1 ) in the open unit disc using the two-sided inequality for the Fox–Wright functions that has been proved by Pogány and Srivastava in (Comput. Math. Appl. 57(1):127–140, 2009). Further, the orders of starlikeness and convexity are also evaluated using some classical tools. We then compare the orders of starlikeness and convexity given by both techniques to illustrate the efficacy of the approach. In addition, we proved that for some values of α, if $\lambda >-1$ λ > − 1 then $\operatorname{Re} (\mathfrak{J}_{\nu ,\lambda }^{\mu ,m}(z)/z )>\alpha $ Re ( J ν , λ μ , m ( z ) / z ) > α , $z\in \mathbb{U}$ z ∈ U , and if $\lambda \ge (\sqrt{10}-6 )/4$ λ ≥ ( 10 − 6 ) / 4 then the function $(\mathfrak{J}_{\nu ,\lambda }^{\mu ,m}(z^{2})/z )\ast \sin z$ ( J ν , λ μ , m ( z 2 ) / z ) ∗ sin z is close-to-convex with respect to $1/2\log ((1+z)/(1-z) )$ 1 / 2 log ( ( 1 + z ) / ( 1 − z ) ) where ∗ stands for the Hadamard product (or convolution) of two power series.

In this work, we apply generalized Saigo fractional differential and integral operators having $ k $-hypergeometric function as a kernel, to extended Lommel-Wright function. The results are communicated in the form of the k-Wright function and are utilized to compute beta transform. The novelty and the generalization of the obtained results are shown by relating them with existing literature as special cases.

Solving a linear partial differential equation witness a noteworthy role of Wright function. Due to its usefulness and various applications, a variety of its extentions (and generalizations) have been investigated and presented. The purpose and design of the paper is intended to study and come up with a new extention of the genralized Wright function by using generalized beta function and obtain some integral representation of the freshly defined function. Also we present the Mellin transform of this function in the form of Fox Wright function. Furthermore, we obtain the recurrence relation, derivative formula for the said function and also by using an extended Riemann-Liouville fractional derivative, we present a fractional derivative formula for the extended Wright function.

The main purpose of the present paper is to determine the radii of starlikeness and convexity associated with lemniscate of Bernoulli and the Janowski function, $(1+Az)/(1+Bz)$ for $-1\leq B, Comment: arXiv admin note: substantial text overlap with arXiv:1911.07901

In this paper, we examine properties of an entire function that is a generalization of the Wright function. Various representations, estimates, and differentiation formulas are obtained.

In this article, the k-fractional-order integral and derivative operators including the k-hypergeometric function in the kernel are used for the k-Wright function; the results are presented for the k-Wright function. Also, some of special cases related to fractional calculus operators and k-Wright function are considered.

Expected utility theory with a smooth utility function predicts that, when allocating wealth between a risky and a riskless asset, investors allocate a positive amount to the risky asset whenever its expected return exceeds the riskless rate of return. A large number of people invest none of their wealth in risky assets, though, leading to the ”participation puzzle.” This paper explores whether the participation puzzle can be addressed when the utility function has a kink at the reference wealth level. It shows that when the reference wealth level is initial wealth increased by the riskless rate of return, there exists a range of expected excess returns for the risky asset for which the investor takes no position. Moreover, this range of expected excess returns is described by comparing a common performance measure of stock returns, the Omega Function, to a function of preference parameters. However, if the reference wealth level is any other constant, the usual expected utility prediction holds and investors allocate at least some of their wealth to the risky asset whenever it has a positive expected excess return.

The prime purpose of this article aims to establish connections between various sub-classes of harmonic univalent mappings by applying a convolution operator associated with the well-known Wright f...

This article aims to establish certain image formulas associated with the fractional calculus operators with Appell function in the kernel and Caputo-type fractional differential operators involving Srivastava polynomials and extended Mittag-Leffler function. The main outcomes are presented in terms of the extended Wright function. In addition, along with the noted outcomes, the implications are also highlighted.

In that resurch work, we find a relation of generalized fractional ABR derivative with well known k-Wright function which is defined for the variable z ∈ C, ai , bj ∈ C, βj, , by the series . We ha...

This paper discusses formulation of the constitutive model for ductile fracture prediction in large-scale metal structures that can be approximated using shell mechanics. One of the primary considerations is the issue of bridging the length scales between micromechanical phenomena governing ductile fracture (i.e. void nucleation, growth and coalescence), which occurs on the scale of several micrometers, and large scale industrial applications. A micromechanics-based shear-modified Gurson model is used as a reference for the proposed formulation. The model is simplified and implemented in generalized plane stress state, with only the most relevant phenomena considered. Bridging of the length scales is achieved through the calibration function that approximates exponential damage growth after the onset of localized neck that cannot be explicitly represented with shell elements. The resulting formulation is a phenomenological three invariant plasticity model with a scalar damage variable dependent on the volumetric plastic strain and deviatoric plastic work. The latter term is dependent on the Nahshon-Hutchinson omega function, which is based on a normalized Lode angle. The model is used to simulate a response of a hat-shaped high strength steel automotive component under three-point bending. Calibration of the model parameters is performed based on uniaxial and plane-strain tensile tests. Close correlation between experimental and analysis results are achieved validating the assumptions and proposed formulation.

Research applying the behavioral economic demand framework is increasingly conducted across disciplines. With respect to psychopharmacology and substance abuse, real and hypothetical purchase tasks are regularly used to evaluate the demand for various substances and reinforcers, such as alcohol. At present, a variety of methods has been introduced to solve for the point of unit elasticity, or Pmax, in the exponential model of demand; however, these methods vary in their potential for error. Current methods for determining Pmax are presented here and a novel exact solution for Pmax in the exponential model of demand is introduced. This solution provides an exact calculation of Pmax using the omega function, as algebraic solutions are not possible. This novel approach is introduced, discussed, and systematically compared to earlier methods for determining Pmax using computer simulations and reanalyses of published study data. Systematic comparison indicated that this new approach, an exact analytic solution for Pmax, provides results that are identical to computationally intensive Pmax methods that directly evaluate the slope of the demand function. The exact analytic Pmax approach is reviewed, its calculations explained, and an easy-to-use web tool is provided to assist researchers in easily performing this calculation of Pmax. Implications for reducing potential sources of error are reviewed and future directions are also discussed. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

A new operator n n n n f z z a z n n ( ) 4 ( ) ( ( 1) ) , 2 ( 1) 1 ( )               W    is introduced for functions of the form   n n n f z  z   a z  2 which are analytic in the open unit disk U  z C: z 1 . We introduce several inclusion properties of the new k-uniformly classes US ;k;   , UC;k; , UK;k; ,  and UK ;k; ,  of analytic functions defined by using the Wright function with the operator  W, and the main object of this paper is to investigate various inclusion relationships for these classes. In addition, we proved that a special property is preserved by some integral operators.

The aim of this article is to establish some integral transforms of the generalized Lommel-Wright functions, which are expressed in terms of Wright Hypergeometric function. Some integrals involving trigonometric, generalized Bessel and Struve functions are also indicated as special cases of our main results.

In this paper, we consider a non-homogeneous time-space-fractional telegraph equation in n-dimensions, which is obtained from the standard telegraph equation by replacing the first- and second-order time derivatives by Caputo fractional derivatives of corresponding fractional orders, and the Laplacian operator by a fractional Sturm-Liouville operator defined in terms of right and left fractional Riemann-Liouville derivatives. Using the method of separation of variables, we derive series representations of the solution in terms of Wright functions, for the homogeneous and non-homogeneous cases. The convergence of the series solutions is studied by using well known properties of the Wright function. We show also that our series can be written using the bivariate Mittag-Leffler function. In the end of the paper, some illustrative examples are presented. info:eu-repo/semantics/publishedVersion

The aim of the paper is to derive certain formulas involving integral transforms and a family of generalized Wright functions, expressed in terms of the generalized Wright hypergeometric function and in terms of the generalized hypergeometric function as well. Based on the main results, some integral formulas involving different special functions connected with the generalized Wright function are explicitly established as special cases for different values of the parameters. Moreover, a Gaussian quadrature formula has been used to compute the integrals and compare with the main results by using graphical representations.

In this chapter, a new four-parameter probability distribution function is introduced and some of its applications are discussed. As the novel distribution function is so flexible that it may be viewed as an alternative to some notable distribution functions, we will call it the pliant distribution function. The cumulative distribution function of the novel probability distribution is founded on the so-called omega function.

This study provides a unified presentation of thermoluminescence (TL) glow-curve deconvolution within the framework of the open source R package "tgcd", according to various analytical expressions that describe first-, second-, general-, and mixed-order kinetics as well as the recently developed semi-analytical expressions that derive from the one trap-one recombination center (OTOR) model that utilizes the Lambert W function or the Wright Omega function. We provide a comprehensive, flexible, convenient, and openly accessible program to analyze TL glow curves according to different models and expressions. The consistency of kinetic parameters determined using different model expressions was assessed using measured TL glow curve of CaF2:Dy. The performance of the computerized glow curve deconvolution (CGCD) method was also tested using simulated glow curves. Results revealed the benefits of comparing kinetic parameters determined from different model expressions and those obtained using experimental TL evaluation methods to assess the reliability of deconvolution results. The accuracy of the CGCD method is dependent upon both the model expressions used and the intrinsic trapping parameters of the TL material.

In this paper, our aim is to show some mean value inequalities for the Fox–Wright function. In order to prove our main results, we present some monotonicity, convexity and concavity properties for some classes of functions related to the Fox–Wright function, which are in fact equivalents to the corresponding Turan type inequalities for this function. As a direct consequences, it deduces some new results involving some special functions, such as the generalized hypergeometric function, the four parameters Wright function and three parameter Mittag–Leffler type function. At the end of this paper, several integrals inequalities associated to the Fox–Wright function are established. As applications, new functional inequalities (such as Turan-type inequalities) for the incomplete Fox–Wright and incomplete generalized hypergeometric functions are established.

In this paper, we give some sufficient conditions for the univalence of some integral operators. For this, we use the Becker's and generalized version of the well known Ahlfor's and Becker's univalence criteria.

In this survey paper, we present both some basic properties of the four-parameters Wright function and its applications in Fractional Calculus. For applications in Fractional Calculus, the four-parameters Wright function of the second kind is especially important. In the paper, three case studies illustrating a wide spectrum of its applications are presented. The first case study deals with the scale-invariant solutions to a one-dimensional time-fractional diffusion-wave equation that can be represented in terms of the Wright function of the second kind and the four-parameters Wright function of the second kind. In the second case study, we consider a subordination formula for the solutions to a multi-dimensional space-time-fractional diffusion equation with different orders of the fractional derivatives. The kernel of the subordination integral is a special case of the four-parameters Wright function of the second kind. Finally, in the third case study, we shortly present an application of an operational calculus for a composed Erdélyi-Kober fractional operator for solving some initial-value problems for the fractional differential equations with the left- and right-hand sided Erdélyi-Kober fractional derivatives. In particular, we present an example with an explicit solution in terms of the four-parameters Wright function of the second kind.

International audience; Using only a limited number of computationally expensive functions, we show a way how to construct accurate and computationally efficient approximations of the Colebrook equation for flow friction based on the asymptotic series expansion of the Wright ω-function and on symbolic regression. The results are verified with 8 million of Quasi-Monte Carlo points covering the domain of interest for engineers. In comparison with the built-in “wrightOmega” feature of Matlab R2016a, the herein introduced related approximations of the Wright ω-function significantly accelerate the explicit solution of the Colebrook equation. Such balance between speed and accuracy could be achieved only using symbolic regression, a computational intelligence approach that can find optimal coefficients and the best structure of the equation. The presented numerical experiments show that the novel symbolic regression approximation reduced the maximal relative error from 0.045% to 0.00337%, i.e. more than 13 times, even the complexity remains almost unchanged. Moreover, we also provide a novel highly precise symbolic regression approximation (max. relative error 0.000024%), which, for the same speed as asymptotic expansion, reduces the relative error by factor 219. This research is motivated by estimation of flow rate using electrical parameters of pumps where direct measurement is not always possible such as in offshore underwater pipelines.

In this paper, using the Mellin transform of Wright function we derive an addition formula for the Wright function. In some special cases, addition formulas for the Hermite, Bessel and Mittag-Leffl...

The aim of this article is to establish a new class of unified integrals associated with the generalized Lommel-Wright functions, which are expressed in terms of the Wright Hypergeometric function. Some integrals involving trigonometric, generalized Bessel function and Struve functions are also indicated as special cases of our main results

In this paper, using the exponential conformal map for the Hankel contour we show a new Schlafli-type integral representation for the Wright function. We apply the steepest descent method and the Lagrange expansion to find the asymptotic expansions of Wright function for the large parameter. We study two cases for the stationary points and discuss the associated asymptotic expansions. The results extend the asymptotic expansions of the Bessel functions of the first and second kinds.

Рассматривается уравнение дробной диффузии с сингулярным оператором Бесселя, действующим по пространственной переменной, и оператором дробного дифференцирования Римана - Лиувилля, действующим по временной переменной. Когда порядок дробной производной равен единице, а особенность у оператора Бесселя отсутствует, рассматриваемое уравнение совпадает с классическим уравнением теплопроводности. Ранее для уравнения дробной диффузии с оператором Бесселя было построено решение задачи Коши и доказана теорема единственности решения в классе функций экспоненциального роста. Построен пример, показывающий, что увеличение показателя степени в условии, гарантирующем единственность решения задачи Коши, влечет за собой неединственность решения. С помощью известных свойств функции Райта получены оценки для построенной функции. Показывается, что она, будучи не равной тождественно нулю, удовлетворяет однородному уравнению и однородному условию Коши.

In this paper, we analyze the effects of Dufour number and fractional-order derivative on unsteady natural convection flow of a viscous and incompressible fluid over an infinite vertical plate with constant heat and mass fluxes. The fractional constitutive model is obtained using fractional calculus approach. The Caputo fractional derivative operator is used in this problem. The dimensionless system of equations has been solved by employing Laplace transformation technique. Closed form solutions for concentration, temperature and velocity are presented in the form of Wright function and complementary error function. Effects of fractional and physical parameters on temperature and velocity profiles are illustrated graphically.

In this paper, we introduced the Mainardi beam and indicated its attributes under the Fractional Fourier transform for power variations of Fractional Fourier transform. The results represent that the behavior of the Mainardi beam is similar to that of the Airy beam. The obtained formula is a very powerful tool to describe propagation of a Mainardi beam through the FFT and the FrFT systems. An analytical expression of the Mainardi beam passing through an Fractional Fourier transform system presented. The influences of the Fractional Fourier transform, rational order of the Mittag-Leffler function (Fourier transform of the Mainardi function) on the normalized intensity distribution and characteristics of the Mainardi beam in the Fractional Fourier transform system examined. Power of the Fractional Fourier transform (p) and rational order of the Mittag-Leffler function (q) control characteristics of the Mainardi beam such as effective beam size, number, width, height, and orientation of the beam spot.

This paper deals with the approximate controllability of a class of non-instantaneous impulsive hybrid systems for fractional differential inclusions under Hilfer derivative of order 1 σ 2 and type 0 ≤ ζ ≤ 1 , on weighted spaces. As an alternative to the Wright function which is defined only when 0 σ 1 , we make use of a family of general fractional resolvent operators to give a proper form of the mild solution. This latter is consequently formulated by Laplace transform, improving and extending important results on this topic. Based on known facts about fractional calculus and set-valued maps, properties of the resolvent operator, and a hybrid fixed point theorem for three operators of Schaefer type, the existence result and the approximate controllability of our system is achieved. An example is given to demonstrate the effectiveness of our result.

We consider the partial differential equation of a mathematical model proposed by Sharmaet al. [1] to describe the concentration of nutrients in blood, a factor which influences erythrocytesedimentation rate. Introducing in it a fractional derivative in the Caputo sense, we create a new, timefractionalmathematical model which contains, as a particular case, the original model. We obtainan analytic solution of this time-fractional partial differential equation in terms of Mittag-Leffler andWright functions and to show that our model is more realistic than the Sharma model.

We construct an explicit representation of the solution of a multidimensional Abel integral equation of the second kind with partial fractional integrals in terms of the Wright function.

In the present paper, we investigate certain geometric properties and inequalities for the Wright function and mention a few important consequences of our main results. A nonlinear differential equation involving the Wright function is also investigated.

In this present paper, we investigate generalized integration formulas containing the generalized $k$-Bessel function $W_{v,c}^{k}(z)$ based on the well known Oberhettinger formula [12] and obtain the results in term of Wright-type function. Also, we establish certain special cases of our main result.

A fractional model of Casson fluid coupled with energy equation is developed. Casson fluid in the presence of heat transfer is considered over an oscillating vertical plate with constant wall temperature. Definition of fractional Caputo derivative is used in the mathematical formulation of the problem. Exact solutions via Laplace transform are obtained and presented in terms of Wright function. Parametric studies were undertaken, and the obtained solutions are illustrated through plots for various physical parameters.

In the present work we introduce a composition formula of the pathway fractional integration operator with finite product of generalized K-Wright function and K4-function. The obtained results are in terms of generalized Wright function.Certain special cases of the main results given here are also considered to correspond with some known and new (presumably) pathway fractional integral formulas.