Fractional Differintegral Operator Research Articles

On Certain Subclass of Meromorphic Multivalent Functions Associated with Fractional Calculus Operator

In this paper, the class of meromorphic multivalent functions of the form by using fractional differ-integral operators is introduced. We get Coefficients estimates, radii of convexity and star likeness. Also closure theorems and distortion theorem for the class , is calculaed.

Application of Fractional Calculus to Establish Equations of State for Solid Metals

Fractional differ-integral operators are used to obtain the equation of state for a substance that can be seen as fractal. Two equations of state have been obtained, the first of which depends on two parameters that characterize the fractal dimension of the material and the thermal energy of the particles, respectively. The second equation involves three parameters, and expressions for the Helmholtz free energy and the bulk modulus have also been obtained for this equation. The model presented in this study has been validated using experimental data available in literature, and fractional exponent have been determined for various metals.

A non-field analytical method for gas dissolution under forced compression

This paper presents an extension of the non-field analytical method—known as the method of Kulish—to model gas dissolution into a liquid due to forced compression. Solutions are obtained for the time evolution of pressure (and, hence, mass concentration) at the gas–liquid interface. These solutions are in the form of series with respect to fractional differ-integral operators. The asymptotic solutions for the two limiting cases of compression—slow and fast compression—have been established as well. Then several particular examples of the law of gas volume variation are considered. Among them, the law of a linear volume variation is the most interesting for practical purposes, in which case numerical values of the dimensionless pressure as a function of dimensionless time are provided.

Certain implementations in fractional calculus operators involving Mittag-Leffler-confluent hypergeometric functions

The Mittag-Leffler function and confluent hypergeometric functions were created to approximate interpolation in exponential functions. The researchers noted that Prabhakar’s integral transformation, which involves extended multi-parameter Mittag-Leffler functions, may be used to create and explore different fractional calculus models. This four-parameter function is further illustrated in graphs using MATLAB. With classical (Riemann–Liouville) fractional integrals, the research shows a set of formulations for these fractional differintegral operators. Moreover, using AB Model results of Prabhakar and the generalized Prabhakar models, the authors use a series of formulae to come up with new results. This paper demonstrates how this series formula may be used to provide simple alternative evidence for numerous well-known effects of Prabhakar differintegrals.

On subclass of analytic univalent functions defined by fractional differ-integral operator I

In this paper , we studied and introduced a new subclass of analytic univalent functions defined by differ – integral operator . We obtain distortion bounds, extreme points , and some theorem of this subclass .

A Grunwald–Letnikov based Manta ray foraging optimizer for global optimization and image segmentation

This paper presents a modified version of Manta ray foraging optimizer (MRFO) algorithm to deal with global optimization and multilevel image segmentation problems. MRFO is a meta-heuristic technique that simulates the behaviors of manta rays to find the food. MRFO established its ability to find a suitable solution for a variant of optimization problems. However, by analyzing its behaviors during the optimization process, it is observed that its exploitation ability is less than exploration ability, which makes MRFO more sensitive to attractive to a local point. Therefore, we enhanced MRFO by using the fractional-order (FO) calculus during the exploitation phase. We used the heredity and non-locality properties of the Grunwald–Letnikov fractional differ-integral operator to simulate the after effect of the previous locations of manta rays on their future movement directions. The proposed Fractional-order MRFO (FO-MRFO) quality is confirmed using a set of two experimental series. Firstly, it is applied to find the solution for CEC2017 benchmark functions with different dimensions of 10, 30, and 50. Through performing the non-parametric statistical analysis, the FO-MRFO shows its superiority in comparison with the basic MRFO. For the second series of experiments, the developed algorithm is implemented as a multilevel threshold image segmentation technique. In this experiment, a variant of natural images is used to assess FO-MFRO. According to different performance measures, the FO-MRFO outperforms the compared algorithms in the global optimization and image segmentation.

Optimal Digital Implementation of Fractional-Order Models in a Microcontroller.

The growing number of operations in implementations of the non-local fractional differentiation operator is cumbersome for real applications with strict performance and memory storage requirements. This demands use of one of the available approximation methods. In this paper, the analysis of the classic integer- (IO) and fractional-order (FO) models of the brushless DC (BLDC) micromotor mounted on a steel rotating arms, and next, the discretization and efficient implementation of the models in a microcontroller (MCU) is performed. Two different methods for the FO model are examined, including the approximation of the fractional-order operator () using the Oustaloup Recursive filter and the numerical evaluation of the fractional differintegral operator based on the Grünwald–Letnikov definition and Short Memory Principle. The models are verified against the results of several experiments conducted on an ARM Cortex-M7-based STM32F746ZG unit. Additionally, some software optimization techniques for the Cortex-M microcontroller family are discussed. The described steps are universal and can also be easily adapted to any other microcontroller. The values for integral absolute error (IAE) and integral square error (ISE) performance indices, calculated on the basis of simulations performed in MATLAB, are used to evaluate accuracy.

Applications of differential subordinations involving a generalized fractional differintegral operator

Using the third-order differential subordination basic results, we introduce certain classes of admissible functions and investigate some applications of third-order differential subordination for p-valent functions associated with generalized fractional differintegral operator.

The Principle of Differential Subordination and Its Application to Analytic and p-Valent Functions Defined by a Generalized Fractional Differintegral Operator

A useful family of fractional derivative and integral operators plays a crucial role on the study of mathematics and applied science. In this paper, we introduce an operator defined on the family of analytic functions in the open unit disk by using the generalized fractional derivative and integral operator with convolution. For this operator, we study the subordination-preserving properties and their dual problems. Differential sandwich-type results for this operator are also investigated.

Subordination and inclusion theorems for higher order derivatives of a generalized fractional differintegral operator

The main object of this paper is to investigate some subordination results of certain subclasses of multivalent analytic functions which are defined by a generalized fractional differintegral operator. Inclusion relations for functions in the class mathcal {S}_{p,q}^{lambda,mu,eta }left (zeta ;A,Bright) and the images of these functions by the generalized Bernardi-Libera-Livingston integral operator are also considered.

Fractional differential and integral operations via cumulative approach

In this study, a fractal operator model of cumulative processes is described. Accordingly, differential and integral operators of the fractional calculus are derived by the fractal operator model of a cumulative process. In order to exhibit the relation between our cumulative approach and fractional calculus, vertical motion of a body is handled within these frameworks. Thereby, regard to our assessments, the underlying physical mechanism of the success of the fractional differintegral operators in describing stochastic complex systems is uncovered to some extent.

Subordination Properties for Multivalent Functions Associated with a Generalized Fractional Differintegral Operator

Using of the principle of subordination, we investigate some subordination and convolution properties for classes of multivalent functions under certain assumptions on the parameters involved, which are defined by a generalized fractional differintegral operator under certain assumptions on the parameters involved.

On a New Class of Meromorphic Multivalent Functions Defined by Fractional Differ-integral Operator

In this work, we submite and study a newlclass of meromorphiccmultivalent functions defined by fractional differ-integral operator . We gain some geometric properties , such as, coefficient inequality, growth and distortion bounds, convolution properties, integral representation, radii of starlikeness and convexity, extreme points, weighted mean and arithmetic mean for functions belonging to the class

Subordinating results for p-valent functions associated with the Srivastava–Saigo–Owa fractional differintegral operator

In this paper, by making use of the principle of subordination, we investigate some subordination and convolution properties of certain subclasses of\(\ p\)-valent analytic functions which are defined by the Srivastava–Saigo–Owa fractional differintegral operator.

Inclusion relations for subclasses of multivalent functions defined by Srivastava–Saigo–Owa fractional differintegral operator

The purpose of this paper is to introduce subclasses of multivalent functions by using Srivastava–Saigo–Owa fractional differintegral operator and investigate various properties for these subclasses. Also, we investigate inclusion relations involving the operator \(F_{p,c}\).

Multivalent functions associated with Srivastava–Saigo–Owa fractional differintegral operator

The purpose of the present paper is to investigate some subordination and other properties of several subclasses of multivalent functions which are defined by the Srivastava–Saigo–Owa fractional differintegral operator. Inclusion relations for functions in the class $$\mathcal {S}_{p,\lambda ,\mu ,\eta }^{m,\delta ,\zeta }(\alpha; A, B)$$ and the images of these functions by the generalized Bernardi–Libera–Livingston integral operator are also considered.

Some properties of certain extended fractional differintegral operator

In this paper, we derive some inequality properties, convolution properties, subordination and superordination properties, and sandwich-type results involving certain extended fractional differintegral operator.

GENERALIZED FRACTIONAL DIFFERINTEGRAL OPERATORS OF THE K-SERIES

In the present paper, we further study the generalized fractional differintegral (integral and differential) operators involving Appell's function <TEX>$F_3$</TEX> introduced by Saigo-Maeda [9], and are applied to the K-Series defined by Gehlot and Ram [3]. On account of the general nature of our main results, a large number of results obtained earlier by several authors such as Ram et al. [7], Saxena et al. [14], Saxena and Saigo [15] and many more follow as special cases.

Inclusion results for certain classes of analytic functions associated with a new fractional differintegral operator

By using a new fractional differintegral operator which was studied in a recent work (Mediterr J Math 13:1535–1553 2016), we first introduce various classes of analytic functions in terms of the subordination and then prove several inclusion results for each of these classes of analytic functions. We also consider some useful special cases and consequences of the results which are presented in this paper.

Some Geometric Properties of Analytic Functions Involving a New Fractional Operator

In this paper, we introduce and study a new fractional operator and its implications in terms of the Ruscheweyh derivative operator, the Sălăgean operator and a certain fractional differintegral operator. Some geometric properties of the analytic functions involving this operator are derived. We also consider some applications and derive certain corollaries of our main results. Some useful consequences and relationship of certain results with known results are also pointed out.