scholarly journals On new applications of fractional calculus

2017 ◽  
Vol 37 (3) ◽  
pp. 113-118 ◽  
Author(s):  
Shilpi Jain ◽  
Praveen Agarwal
Keyword(s):  
Fractional Calculus ◽  
Special Functions ◽  
Leibniz Rule ◽  
The One ◽  
New Applications ◽  
Paper Author

In the present paper author derive a number of integrals concerning various special functions which are applications of the one of Osler result. Osler provided extensions to the familiar Leibniz rule for the nth derivative of product of two functions.

The mellin integral transform in fractional calculus

2013 ◽  
Vol 16 (2) ◽  
Author(s):  
Yuri Luchko ◽  
Virginia Kiryakova
Keyword(s):  
Fractional Calculus ◽  
Fourier Transforms ◽  
Integral Transform ◽  
Special Functions ◽  
Integral Transforms ◽  
Fourier Integral ◽  
Monotone Functions ◽  
Completely Monotone ◽  
Mellin Convolution ◽  
New Applications

AbstractIn Fractional Calculus (FC), the Laplace and the Fourier integral transforms are traditionally employed for solving different problems. In this paper, we demonstrate the role of the Mellin integral transform in FC. We note that the Laplace integral transform, the sin- and cos-Fourier transforms, and the FC operators can all be represented as Mellin convolution type integral transforms. Moreover, the special functions of FC are all particular cases of the Fox H-function that is defined as an inverse Mellin transform of a quotient of some products of the Gamma functions.In this paper, several known and some new applications of the Mellin integral transform to different problems in FC are exemplarily presented. The Mellin integral transform is employed to derive the inversion formulas for the FC operators and to evaluate some FC related integrals and in particular, the Laplace transforms and the sin- and cos-Fourier transforms of some special functions of FC. We show how to use the Mellin integral transform to prove the Post-Widder formula (and to obtain its new modi-fication), to derive some new Leibniz type rules for the FC operators, and to get new completely monotone functions from the known ones.

scholarly journals Fredholm type integral equation with special functions

2018 ◽  
Vol 10 (1) ◽  
pp. 5-17 ◽  
Author(s):  
Frdric Ayant ◽  
Dinesh Kumar
Keyword(s):  
Integral Equation ◽  
Fractional Calculus ◽  
Special Functions ◽  
Fredholm Type ◽  
One Dimensional ◽  
Type Integral ◽  
The One ◽  
Dimensional Integral

Abstract Recently Chaurasia and Gill [7], Chaurasia and Kumar [8] have solved the one-dimensional integral equation of Fredholm type involving the product of special functions. We solve an integral equation involving the product of a class of multivariable polynomials, the multivariable H-function defined by Srivastava and Panda [29, 30] and the multivariable I-function defined by Prasad [21] by the application of fractional calculus theory. The results obtained here are general in nature and capable of yielding a large number of results (known and new) scattered in the literature.

scholarly journals New fractional approaches for n-polynomial P-convexity with applications in special function theory

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shu-Bo Chen ◽  
Saima Rashid ◽  
Muhammad Aslam Noor ◽  
Zakia Hammouch ◽  
Yu-Ming Chu
Keyword(s):  
Fractional Calculus ◽  
Convex Functions ◽  
Special Functions ◽  
Real Life ◽  
Fractional Integrals ◽  
Digamma Function ◽  
Novel Approach ◽  
Inequality Theory ◽  
New Strategy ◽  
Significant Mechanism

Abstract Inequality theory provides a significant mechanism for managing symmetrical aspects in real-life circumstances. The renowned distinguishing feature of integral inequalities and fractional calculus has a solid possibility to regulate continuous issues with high proficiency. This manuscript contributes to a captivating association of fractional calculus, special functions and convex functions. The authors develop a novel approach for investigating a new class of convex functions which is known as an n-polynomial $\mathcal{P}$ P -convex function. Meanwhile, considering two identities via generalized fractional integrals, provide several generalizations of the Hermite–Hadamard and Ostrowski type inequalities by employing the better approaches of Hölder and power-mean inequalities. By this new strategy, using the concept of n-polynomial $\mathcal{P}$ P -convexity we can evaluate several other classes of n-polynomial harmonically convex, n-polynomial convex, classical harmonically convex and classical convex functions as particular cases. In order to investigate the efficiency and supremacy of the suggested scheme regarding the fractional calculus, special functions and n-polynomial $\mathcal{P}$ P -convexity, we present two applications for the modified Bessel function and $\mathfrak{q}$ q -digamma function. Finally, these outcomes can evaluate the possible symmetric roles of the criterion that express the real phenomena of the problem.

scholarly journals Some New Fractional-Calculus Connections between Mittag–Leffler Functions

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 485 ◽  
Author(s):  
Hari M. Srivastava ◽  
Arran Fernandez ◽  
Dumitru Baleanu
Keyword(s):  
Experimental Data ◽  
Fractional Calculus ◽  
Fractional Derivative ◽  
Fractional Integral ◽  
Integral Expression ◽  
Potential Applications ◽  
The One ◽  
Two Parameter

We consider the well-known Mittag–Leffler functions of one, two and three parameters, and establish some new connections between them using fractional calculus. In particular, we express the three-parameter Mittag–Leffler function as a fractional derivative of the two-parameter Mittag–Leffler function, which is in turn a fractional integral of the one-parameter Mittag–Leffler function. Hence, we derive an integral expression for the three-parameter one in terms of the one-parameter one. We discuss the importance and applications of all three Mittag–Leffler functions, with a view to potential applications of our results in making certain types of experimental data much easier to analyse.

How can health professionals contribute to the internet of things body of knowledge

2019 ◽  
Vol 49 (2) ◽  
pp. 229-240 ◽  
Author(s):  
Mehdi Dadkhah ◽  
Mohammad Lagzian ◽  
Gabriele Santoro
Keyword(s):  
Internet Of Things ◽  
Health Professionals ◽  
Design Methodology ◽  
Content Type ◽  
Technological Paradigm ◽  
Body Of Knowledge ◽  
The One ◽  
New Applications ◽  
Technical People ◽  
The Internet Of Things

Purpose Internet of Things (IoT) as the new technological paradigm has found many applications in different domains. Nowadays, more than 30,000 records related to IoT research can be accessed in Scopus (Scopus.com). Health care is the one of domains which benefits from IoT. However, observations indicate that most active researchers in this area are technical people not health professionals. The purpose of this paper is to understand how health professionals can contribute to the IoT body of knowledge. Design/methodology/approach IoT professionals are asked to provide their views regarding research concerns, and the collected data are analyzed by phenomenography research methodology. Findings Findings indicate that health professionals can contribute through providing information, requirement or standards for developing IoT systems or devices. They can also introduce new applications or domains for which IoT is fit. Originality/value This paper tries to fill the gap concerning the lack of attention to undertaking IoT-related research from health professionals’ side and highlights ways that health professionals can contribute IoT body of knowledge.

Analysis of flowrates as a basis for the simulation of dry-running rotational positive displacement pumps

2002 ◽  
Vol 216 (12) ◽  
pp. 1197-1205 ◽  
Author(s):  
K Kauder ◽  
D Wenderott
Keyword(s):  
Mass Flow ◽  
Characteristic Number ◽  
Operational Reliability ◽  
Simulation System ◽  
Positive Displacement ◽  
Market Situation ◽  
Flow Through ◽  
The One ◽  
New Applications ◽  
Operational Behaviour

New applications improve the market situation of dry-running positive displacement pumps. The mostly empirically based design of these pumps has to take into account partly competing viewpoints. These viewpoints are energetic process optimization, on the one hand, and operational reliability, on the other hand. A simulation system can be used to solve this problem. The simulation system uses an energy and a mass balance in order to simulate the operational behaviour of the vacuum pumps. Therefore knowledge of the different states of flow through clearances in a vacuum is essential. The experimental examination of the flow is done by flood curve measurements, to describe the mass flow integrally using the characteristic number of the standardized mass flow. The results for some possible plain clearance shapes are discussed.

scholarly journals REPRESENTATIONS OF sl(2) IN THE BOOLEAN LATTICE, AND THE HAMMING AND JOHNSON SCHEMES

2012 ◽  
Vol 15 (03) ◽  
pp. 1250019
Author(s):  
PHILIP FEINSILVER
Keyword(s):  
Special Functions ◽  
Regular Representation ◽  
Boolean Lattice ◽  
Irreducible Representations ◽  
Leibniz Rule ◽  
Krawtchouk Polynomials ◽  
Lattice Representation ◽  
Boolean Poset ◽  
Group Law

Starting with the zero-square "zeon algebra," the regular representation gives rise to a Boolean lattice representation of sl(2). We detail the su(2) content of the Boolean lattice, providing the irreducible representations carried by the algebra generated by the subsets of an n-set. The group elements are found, exhibiting the "special functions" in this context. The corresponding Leibniz rule and group law are shown. Krawtchouk polynomials, the Hamming and the Johnson schemes appear naturally. Applications to the Boolean poset and the structure of Hadamard–Sylvester matrices are shown as well.

Applications of the fractional calculus to study the physical theory of ion motion in a quadrupole ion trap

2017 ◽  
Vol 23 (5) ◽  
pp. 254-271 ◽  
Author(s):  
Sarkhosh S Chaharborj ◽  
Abbas Moameni
Keyword(s):  
Fractional Calculus ◽  
Ion Trap ◽  
Three Dimensional ◽  
Quadrupole Ion Trap ◽  
Stability Diagram ◽  
Mass Separation ◽  
Damping Force ◽  
Ion Motion ◽  
The One ◽  
Fractional Parameter

In this article, fractional calculus has been applied to study the motion of ions in a three-dimensional radio frequency quadrupole ion trap; we have called this arrangement a fractional quadrupole ion trap. The main purpose of the article is to show that by controlling the fractional parameter of a trapped ion, one can gain a more efficient mass separation. In what follows, we will see that with decreasing the fractional parameter, we can achieve a smaller first stability region. Note that a small stability diagram will result in a good and acceptable mass separation. Various methods can be proposed to obtain a desired ion acceleration with a sufficient accuracy for good mass separation, which is similar to the one obtained by a fractional ion trap. Some of these methods are using the effects of a damping force, a magnetic field or both on the confinement of particles in the quadrupole ion trap. The first stability regions are plotted for all of the aforementioned methods, and simulation results are provided to compare them with those for the fractional case.

scholarly journals Approximating Ideal Filters by Systems of Fractional Order

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Ming Li
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
Point Of View ◽  
Present Approach ◽  
The Other ◽  
Necessary Condition ◽  
Ecg Signals ◽  
Other Hand ◽  
The One ◽  
Electrocardiogram Ecg

The contributions in this paper are in two folds. On the one hand, we propose a general approach for approximating ideal filters based on fractional calculus from the point of view of systems of fractional order. On the other hand, we suggest that the Paley and Wiener criterion might not be a necessary condition for designing physically realizable ideal filters. As an application of the present approach, we show a case in designing ideal filters for suppressing 50-Hz interference in electrocardiogram (ECG) signals.

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