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Aim: To examine the prevalence of complications related with transulnar approach in patients undergoing elective percutaneous coronary interventions. Study Design: Cross-sectional/observational study. Place & Duration: The study was conducted at cardiology department of Cat A Hospital Batkhela and Fauji Foundation Hospital Peshawar for six months duration from January 2020 to December 2020. Methods: One hundred and eighteen patients of both genders with ages 20 to 75 years who underwent percutaneous coronary interventions were included. Patients’ detailed demographics including age, sex, BMI and com-morbidities were recorded after taking informed written consent from all the patients. All the patients had percutaneous coronary procedure through transulnar approach and periprocedural complications were examined. Data was analyzed using SPSS 24.0. Results: Out of 118 patients 85 (72.03%) were males and 33 (27.97%) were females with mean age of 55.74±11.71 years. Mean BMI was 28.09±7.33 kg/m2. Hypertension was the most common morbidity found in 63 (53.4%) patients followed by diabetes mellitus and smoking. Minor bleeding was the commonest complication found in 28 (23.7%) patients followed by ulnar artery occlusion, excessive bleeding, ulnar nerve injury and hematoma in 10 (8.5%), 8 (6.8%), 6 (5.08%) and 2 (2.5%) patients respectively. Conclusion: It is concluded that transulnar approach for coronary interventions is safe and effective with fewer rate of complications. Keywords: Coronary Intervention, Angiography, Transulnar Approach, Complications.

In modern times, the organizational managements greatly depend on decision-making (DM). DM is considered the management’s fundamental function that helps the businesses and organizations to accomplish their targets. Several techniques and processes are proposed for the efficient DM. Sometimes, the situations are unclear and several factors make the process of DM uncertain. Fuzzy set theory has numerous tools to tackle such tentative and uncertain events. The complex picture fuzzy set (CPFS) is a super powerful fuzzy-based structure to cope with the various types of uncertainties. In this article, an innovative DM algorithm is designed which runs for several types of fuzzy information. In addition, a number of new notions are defined which act as the building blocks for the proposed algorithm, such as information energy of a CPFS, correlation between CPFSs, correlation coefficient of CPFSs, matrix of correlation coefficients, and composition of these matrices. Furthermore, some useful results and properties of the novel definitions have been presented. As an illustration, the proposed algorithm is applied to a clustering problem where a company intends to classify its products on the basis of features. Moreover, some experiments are performed for the purpose of comparison. Finally, a comprehensive analysis of the experimental results has been carried out, and the proposed technique is validated.

In this paper, we study a new class of Hardy-type inequalities involving fractional calculus operators. We derive the Hardy-type inequalities for the variant of Riemann–Liouville fractional calculus operators and [Formula: see text]-Hilfer fractional derivative operator. The obtained inequalities involving fractional operators are more general as compared to some existing results in the literature.

The aim of this paper is to prove some identities in the form of generalized Meijer G -function. We prove the relation of some known functions such as exponential functions, sine and cosine functions, product of exponential and trigonometric functions, product of exponential and hyperbolic functions, binomial expansion, logarithmic function, and sine integral, with the generalized Meijer G -function. We also prove the product of modified Bessel function of first and second kind in the form of generalized Meijer G -function and solve an integral involving the product of modified Bessel functions.

In this present paper we study the non-local Hadmard proportional integrals recently proposed by Rahman et al. (Advances in Difference Equations, (2019) 2019:454) which containing exponential functions in their kernels. Then we establish certain new weighted fractional integral inequalities involving a family of n ( n &isin, N ) positive functions by utilizing Hadamard proportional fractional integral operator. The inequalities presented in this paper are more general than the inequalities existing in the literature.

Since Gruss presented an interesting integral inequality in [9], its various generalizations and variants, which are called Gruss type inequalities, have been investigated. Very recently, certain Gruss type inequalities involving ? ? s , k-fractional integral operator have been established. Motivated by the above mentioned works, we aim to present a Young's type inequality and a weighted AM-GM type inequality involving the ? ? ? , k-fractional integral operator. Some special cases of the main results here are also considered.

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.

In this paper, we present certain composition formulae of the pathway fractional integral operators associated with two extended Mittag-Leffler functions. Here, we find out the relevant connections of some particular cases of the main results with those earlier ones.

This paper is devoted to the study of fractional calculus with an integral and differential operators containing the following family of extended Mittag–Leffler function: $$\begin{aligned} E_{\alpha ,\beta }^{\gamma ;c}(z; p)=\sum \limits _{n=0}^{\infty }\frac{B_p(\gamma +n, c-\gamma )(c)_{n}}{B(\gamma , c-\gamma )\Gamma (\alpha n+\beta )}\frac{z^n}{n!}, (z,\beta , \gamma \in \mathbb {C}), \end{aligned}$$ in its kernel. Also, we further introduce a certain number of consequences of fractional integral and differential operators containing the said function in their kernels.

In this paper, we introduce the $(k, s)$ -fractional integral and differential operators involving k-Mittag-Leffler function $E_{k,\rho,\beta}^{\delta}(z)$ as its kernel. Also, we establish various properties of these operators. Further, we consider a number of certain consequences of the main results.

In this present article, we establish certain new Pólya–Szegö-type tempered fractional integral inequalities by considering the generalized tempered fractional integral concerning another function Ψ in the kernel. We then prove certain new Chebyshev-type tempered fractional integral inequalities for the said operator with the help of newly established Pólya–Szegö-type tempered fractional integral inequalities. Also, some new particular cases in the sense of classical tempered fractional integrals are discussed. Additionally, examples of constructing bounded functions are considered. Furthermore, one can easily form new inequalities for Katugampola fractional integrals, generalized Riemann–Liouville fractional integral concerning another function Ψ in the kernel, and generalized fractional conformable integral by applying different conditions.

In this paper, we define a new extension of Srivastava's triple hypergeometric functions by using a new extension of Pochhammer's symbol that was recently proposed by Srivastava, Rahman and Nisar [H. M. Srivastava, G. Rahman and K. S. Nisar, Some extensions of the Pochhammer symbol and the associated hypergeometric functions, Iran. J. Sci. Technol. Trans. A Sci. 43 2019, 5, 2601-2606]. We present their certain basic properties such as integral representations, derivative formulas, and recurrence relations. Also, certain new special cases have been identified and some known results are recovered from main results. © 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.

Inspired by certain fascinating ongoing extensions of the special functions such as an extension of the Pochhammer symbol and generalized hypergeometric function, we present a new extension of the generalized Mittag-Leffler (ML) function εa,b;p,vκz1 in terms of the generalized Pochhammer symbol. We then deliberately find certain various properties and integral transformations of the said function εa,b;p,vκz1. Some particular cases and outcomes of the main results are also established.

In this paper, we aim to determine some results of the generalized Bessel–Maitland function in the field of fractional calculus. Here, some relations of the generalized Bessel–Maitland functions and the Mittag-Leffler functions are considered. We develop Saigo and Riemann–Liouville fractional integral operators by using the generalized Bessel–Maitland function, and results can be seen in the form of Fox–Wright functions. We establish a new operator Zν,η,ρ,γ,w,a+μ,ξ,m,σϕ and its inverse operator Dν,η,ρ,γ,w,a+μ,ξ,m,σϕ, involving the generalized Bessel–Maitland function as its kernel, and also discuss its convergence and boundedness. Moreover, the Riemann–Liouville operator and the integral transform (Laplace) of the new operator have been developed.

In the paper, the authors establish several new inequalities of the Gruss type for conformable k-fractional integral operators. These inequalities generalize some known results.

Our main goal in this present paper is to define first a new extension of the Pochhammer symbol and the gamma functions which involving the Mittag-Leffler function in their kernels. By using this extended Pochhammer symbol, we then introduce and investigate the corresponding extension of the generalized hypergeometric functions and of some of its special cases. Also, we establish the basic properties and results for the extended $$\tau $$-Gauss hypergeometric function, which includes integral and derivative formulas involving the Mellin transform and fractional calculus approaches. Some new and known results as consequences of our proposed extension of the $$\tau $$-Gauss hypergeometric function are also established.

Since an interesting functional by P.L. Chebyshev was presented in the year 1882, many results, which are called Chebyshev-type inequalities, have been established. Some of these inequalities were obtained by using fractional integral operators. Very recently, a new variant of the fractional conformable integral operator was introduced by Jarad et al. Motivated by this operator, we aim at establishing novel inequalities for a class of differentiable functions, which are associated with Chebyshev&rsquo, s functional, by employing a fractional conformable integral operator. We also aim at showing important connections of the results here with those including Riemann&ndash, Liouville fractional and classical integrals.

Kottakkaran Sooppy Nisar, Feng Qi, Gauhar Rahman, Shahid Mubeen, and Muhammad Arshad, Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric $k$-function, Journal of Inequalities and Applications 2018, Paper No. 135, 12 pages; available online at https://doi.org/10.1186/s13660-018-1717-8.; International audience; In the paper, the authors present some inequalities involving the extended gamma function and the Kummer confluent hypergeometric $k$-function via some classical inequalities such as the Chebychev inequality for synchronous (or asynchronous, respectively) mappings, give a new proof of the log-convexity of the extended gamma function by using the H\"older inequality, and introduce a Tur\'an type mean inequality for the Kummer confluent $k$-hypergeometric function.

In this paper, we define a (p,v)-extension of Hurwitz-Lerch Zeta function by considering an extension of beta function defined by Parmar et al. [J. Classical Anal. 11 (2017) 81–106]. We obtain its basic properties which include integral representations, Mellin transformation, derivative formulas and certain generating relations. Also, we establish the special cases of the main results.

A new generalization of extended beta function and its various properties,integral representations and distribution are given in this paper. In addition, we establishthe generalization of extended hypergeometric and con uent hypergeometric functionsusing the newly extended beta function. The properties these extended and con uenthypergeometric functions such as integral representations, Mellin transformations, dif-ferentiation formulas, transformation and summation formulas are also investigated.

The main objective of this paper is to introduce a further extension of extended (p, q)-beta function by considering two Mittag-Leffler function in the kernel. We investigate various properties of this newly defined beta function such as integral representations, summation formulas and Mellin transform. We define extended beta distribution and its mean, variance and moment generating function with the help of extension of beta function. Also, we establish an extension of extended (p, q)-hypergeometric and (p, q)-confluent hypergeometric functions by using the extension of beta function. Various properties of newly defined extended hypergeometric and confluent hypergeometric functions such as integral representations, Mellin transformations, differentiation formulas, transformation and summation formulas are investigated.

The main objective of this paper is to derive contiguous function relations or recurrence relations and obtain an integral representation Appell k-series F_(1,k), where k>0.

The main objective of this present paper is to introduce further extension of extended Caputo fractional derivative operator and establish the extension of an extended fractional derivative of some known elementary functions. Also, we investigate the extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and generating relations for extension of extended hypergeometric functions.

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to k-hypergeometric and k-Appell's functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

The main objective of this present paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. Also, we give some results related to the newly defined fractional operator such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

In this paper, we pursue and investigate the solutions for fractional kinetic equations, involving Bessel-Struve function by means of their Sumudu transforms. In the process, one Important special case is then revealed, and analyzed. The results obtained in terms of Bessel-Struve function are rather general in nature and can easily construct various known and new fractional kinetic equations.

In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional integral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.

In this note we present some corrections to our previous paper (Nisar et al. in Adv. Differ. Equ. 2017:118, 2017).

The main aim of this paper is to establish two generalized integral formulas involving the extended Mittag–Leffler function based on the well known Lavoie and Trottier integral formula and the obtain results are express in term of extended Wright-type function. Also, we establish certain special cases of our main result.

In this research work, our aim is to determine the contiguous function relations for k-hypergeometric functions with one parameter corresponding to Gauss fifteen contiguous function relations for hypergeometric functions and also obtain contiguous function relations for two parameters. Throughout in this research paper, we find out the contiguous function relations for both the cases in terms of a new parameter k>0. Obviously if k→1, then the contiguous function relations for k-hypergeometric functions are Gauss contiguous function relations.

Recently, different extensions of the fractional derivative operator are found in many research papers. The main aim of this paper is to establish an extension of the extended Caputo fractional derivative operator. The extension of an extended fractional derivative of some elementary functions derives by considering an extension of beta function which includes the Mittag-Leffler function in the kernel. Further, an extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and the generating relations for extension of extended hypergeometric functions also presented in this study.