A Further Extension of the Extended Riemann-Liouville Fractional Derivative Operator

The main objective of this 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. We also give some results related to the newly defined fractional operator, such as Mellin transform and relations to extended hypergeometric and Appell\u27s function via generating functions

Optimal Nonlocal means algorithm for denoising ultrasound image

We propose a new measure for denoising image by calculating mean distance of all pixels in an image in non-local means (NL-means) algorithm. We compute and analyze the original NL-means algorithm which total all the distance of the patches but, our proposed algorithm calculates the mean value of all distance of all the patches and then than get the sum of all distance. Our proposed algorithm exhibit better result with comparison of the existing NL-means algorithm. Keywords: NL-means, Patches, Mean Value, Measurement Matrix

Some properties of generalized (S, k)-bessel function in two variables

The devotion of this paper is to study the Bessel function of two variables in k-calculus. we discuss the generating function of k-Bessel function in two variables and develop its relations. After this we introduce the generalized (s, k)-Bessel function of two variables which help to develop its generating function. The s-analogy of k-Bessel function in two variables is also discussed. Some recurrence relations of the generalized (s, k)-Bessel function in two variables are also derived. © 2022 All rights reserved

Fractional Integration and Solution of Generalized kinetic equation considering Generalized Lommel-Wright function

Abstract.: In this article, we initially built the generalized form of theLommel-Wright function and then evaluated the Saigo hypergeometricfractional integrals of the newly built special function. We developed ageneralized form of the fractional kinetic equation using the introducedspecial function. The solution of the generalized fractional kinetic equationin terms of the Mittag-Leffler functions is established via Laplacetransform. Some special cases are also discussed.AMS (MOS) Subject Classification Codes: 33C70; 26A33; 33C45; 33C60KeyWords: Lommel-Wright k-function; Fractional kinetic equations; Laplace transform;Mittag-Leffler function

Generalization of Chi-square Distribution

In this paper, we define a generalized chi-square distribution by using a new parameter k \u3e 0. we give some properties of the said distribution including the moment generating function and characteristic function in terms of k. Also, we establish a relationship in central moments involving the parameter k \u3e 0. If k = 1, we have all the results of classical c2 distribution

Tempered Fractional Integral Inequalities for Convex Functions

Certain new inequalities for convex functions by utilizing the tempered fractional integral are established in this paper. We also established some new results by employing the connections between the tempered fractional integral with the (R-L) fractional integral. Several special cases of the main result are also presented. The obtained results are more in a general form as it reduced certain existing results of Dahmani (2012) and Liu et al. (2009) by employing some particular values of the parameters

Quantifying the impact of coefficient of thermal expansion of overlay concrete on unbonded concrete overlay performance

With the advancement in pavement design and performance analysis procedures, the coefficient of thermal expansion (CTE) of concrete has emerged as a significant design input with a direct impact on concrete pavement performance parameters including transverse cracking, joint faulting, and pavement roughness. CTE is the measure of change in concrete volume with temperature change and the resulting curling of concrete pavement slab is directly proportional to CTE. Un-Bonded Concrete Overlay (UBCO) is a cost-effective and sustainable rehabilitation technique on Jointed Plain Concrete Pavements (JPCP) to improve the performance of deteriorated concrete pavements. This study examines the effects of variability of CTE on the performance of unbonded JPCP overlays for two different climatic regions. Simulations were conducted using AASHTO pavement ME design software with varying CTE values in the range of 6.8–10.8 micro-strain/°C and keeping all other design variables as constant. The performance predictions were evaluated for different values of CTE and the results indicated that with an increase in CTE value, the performance of UBCO is adversely affected by the increase in pavement distresses. Amongst all the performance parameters, transverse cracking is the most significantly affected parameter with the change in CTE. The impact of geometric properties of overlay pavement including transverse joint spacing and slab thickness on the pavement performance was also analyzed which indicated that these have a direct impact on the performance parameters. The overlay performance can be improved by increased overlay slab thickness or reduced joint spacing and with these modifications, the adverse effects of higher CTE can be compensated. Field performance data of UBCO extracted from the LTPP database showed that the pavement ME design software can accurately predict the performance of UBCO pavement systems

Some new inequalities of the Grüss type for conformable fractional integrals

In the paper, the authors establish some new inequalities of the Grüss type for conformable fractional integrals. These inequalities generalize some known results