scholarly journals Construction of Generalized k-Bessel–Maitland Function with Its Certain Properties

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Waseem Ahmad Khan ◽  
Hassen Aydi ◽  
Musharraf Ali ◽  
Mohd Ghayasuddin ◽  
Jihad Younis
Keyword(s):  
Laplace Transform ◽  
Gamma Function ◽  
Fractional Integration ◽  
Integral Transforms ◽  
Fractional Differentiation ◽  
New Class ◽  
Analytical Properties ◽  
Main Motive

The main motive of this study is to present a new class of a generalized k -Bessel–Maitland function by utilizing the k -gamma function and Pochhammer k -symbol. By this approach, we deduce a few analytical properties as usual differentiations and integral transforms (likewise, Laplace transform, Whittaker transform, beta transform, and so forth) for our presented k -Bessel–Maitland function. Also, the k -fractional integration and k -fractional differentiation of abovementioned k -Bessel–Maitland functions are also pointed out systematically.

INTEGRAL TRANSFORM OF K4-FUNCTION

2021 ◽  
Vol 21 (2) ◽  
pp. 429-436
Author(s):  
SEEMA KABRA ◽  
HARISH NAGAR
Keyword(s):  
Laplace Transform ◽  
Hypergeometric Function ◽  
Integral Transform ◽  
Integral Transforms ◽  
Gauss Hypergeometric Function ◽  
Wright Function ◽  
Generalized Wright Function ◽  
Special Cases ◽  
Euler Transform

In this present work we derived integral transforms such as Euler transform, Laplace transform, and Whittaker transform of K4-function. The results are given in generalized Wright function. Some special cases of the main result are also presented here with new and interesting results. We further extended integral transforms derived here in terms of Gauss Hypergeometric function.

scholarly journals Integral transforms of the κ-Hilfer fractional derivative

2021 ◽  
Author(s):  
Felix Costa ◽  
Junior Cesar Alves Soares ◽  
Stefânia Jarosz
Keyword(s):  
Fractional Derivative ◽  
Gamma Function ◽  
Fundamental Theorem ◽  
Beta Function ◽  
Integral Transforms ◽  
Fractional Operators ◽  
Riesz Fractional Derivative ◽  
Hilfer Fractional Derivative ◽  
Fundamental Theorem Of Calculus

In this paper, some important properties concerning the κ-Hilfer fractional derivative are discussed. Integral transforms for these operators are derived as particular cases of the Jafari transform. These integral transforms are used to derive a fractional version of the fundamental theorem of calculus. Keywords: Integral transforms, Jafari transform, κ-gamma function, κ-beta function, κ-Hilfer fractional derivative, κ-Riesz fractional derivative, κ-fractional operators.

A Fractional Differentiation Theorem for the Laplace Transform

1975 ◽  
Vol 18 (4) ◽  
pp. 605-606 ◽  
Author(s):  
J. Conlan ◽  
E. L. Koh
Keyword(s):  
Laplace Transform ◽  
Systems Analysis ◽  
Inverse Image ◽  
Single Variable ◽  
Fractional Differentiation ◽  
The Laplace Transform ◽  
Differentiation Theorem

In certain systems analysis ([1], [2], [3]), it is essential to invert the n-dimensional Laplace transform and specify the inverse image at a single variable t.

Integral transforms based upon fractional integration

1963 ◽  
Vol 59 (1) ◽  
pp. 63-71 ◽  
Author(s):  
Charles Fox
Keyword(s):  
Functional Equation ◽  
Mellin Transform ◽  
Fourier Transforms ◽  
Fractional Integration ◽  
Integral Transforms ◽  
Image Position

AbstractThe theory of Fourier transformscan be developed from the functional equation K(s) K(1 – s) = 1, where K(s) is the Mellin transform of the kernel k(x).In this paper I show that reciprocities can be obtained which are analogous to the Fourier transforms above but which develop from the much more general functional equationThe reciprocities are obtained by using fractional integration. In addition to the reciprocities we have analogues of the Parseval theorem and of the discontinuous integrals usually associated with Fourier transforms.In order to simplify the analysis I confine myself to the case n = 1 and to L2 space.

scholarly journals Dualities between Elzaki Transform and Some Useful Integral Transforms

2019 ◽  
Vol 8 (12) ◽  
pp. 4312-4318 ◽  
Keyword(s):  
Heat Transfer ◽  
Laplace Transform ◽  
Integral Transforms ◽  
Second Law ◽  
Electrical Networks ◽  
Carbon Dating ◽  
Motion Signal ◽  
Sumudu Transform ◽  
Basic Functions ◽  
Bending Of Beams

Integral transforms have wide applications in the various disciplines of engineering and science to solve the problems of heat transfer, springs, mixing problems, electrical networks, bending of beams, carbon dating problems, Newton’s second law of motion, signal processing, exponential growth and decay problems. In this paper, we will discuss the dualities between Elzaki transform and some useful integral transforms namely Laplace transform, Kamal transform, Aboodh transform, Sumudu transform, Mahgoub (Laplace-Carson) transform, Mohand transform and Sawi transform. To visualize the importance of dualities between Elzaki transform and mention integral transforms, we give tabular presentation of the integral transforms (Laplace transform, Kamal transform, Aboodh transform, Sumudu transform, Mahgoub transform, Mohand transform and Sawi transform) of mostly used basic functions by using mention dualities relations. Results show that the mention integral transforms are strongly related with Elzaki transform

scholarly journals Dualities between Mohand Transform and Some Useful Integral Transforms

2019 ◽  
Vol 8 (3) ◽  
pp. 843-847
Keyword(s):  
Signal Processing ◽  
Laplace Transform ◽  
Exponential Growth ◽  
Integral Transforms ◽  
Second Law ◽  
Electrical Networks ◽  
Carbon Dating ◽  
Sumudu Transform ◽  
Basic Functions ◽  
Bending Of Beams

Integral transforms have wide applications in the different areas of engineering and science to solve the problems of springs, Newton’s law of cooling, electrical networks, bending of beams, mixing problems, signal processing, carbon dating problems, Newton’s second law of motion, exponential growth and decay problems. In this paper, we will discuss the dualities of some useful integral transforms namely Laplace transform, Kamal transform, Elzaki transform, Aboodh transform, Sumudu transform, Mahgoub (Laplace- Carson) transform and Sawi transform with Mohand transform. To visualize the importance of dualities between Mohand transform and mention integral transforms, we give tabular presentation of the integral transforms (Laplace transform, Kamal transform, Elzaki transform, Aboodh transform, Sumudu transform, Mahgoub transform and Sawi transform) of mostly used basic functions by using mention dualities relations.

scholarly journals Absorptive Repetitive Filters with Operators of Generalized Fractional Calculus

2013 ◽  
Vol 13 (4) ◽  
pp. 42-53 ◽  
Author(s):  
Nina Nikolova ◽  
Emil Nikolov
Keyword(s):  
Comparative Analysis ◽  
Fractional Calculus ◽  
Control Systems ◽  
Fractional Order ◽  
Fractional Integration ◽  
Frequency Characteristics ◽  
Rational Approximations ◽  
Integer Order ◽  
New Class ◽  
Generalized Fractional Calculus

Abstract : An essentially new class of repetitive fractional disturbance absorptive filters in disturbances absorbing control systems is proposed in the paper. Systematization of the standard repetitive fractional disturbance absorptive filters of this class is suggested. They use rational approximations of the operators for fractional integration in the theory of fractional calculus. The paper discusses the possibilities for repetitive absorbing of the disturbances with integer order filters and with fractional order filters. The results from the comparative analysis of their frequency characteristics are given below.

scholarly journals Connections between Aboodh Transform and Some Effective Integral Transforms

2019 ◽  
Vol 9 (1) ◽  
pp. 1465-1470
Keyword(s):  
Heat Transfer ◽  
Signal Processing ◽  
Laplace Transform ◽  
Integral Transforms ◽  
Research Paper ◽  
Electrical Networks ◽  
Sumudu Transform ◽  
Transfer Problems ◽  
Bending Of Beams

Integral transforms are the most useful techniques of the mathematics which are used to finding the solution of heat transfer problems, mixing problems, electrical networks, bending of beams, signal processing problems, which generally appears in the various disciplines of engineering and sciences. In this research paper, connections between Aboodh transform and some effective integral transforms (Laplace transform, Kamal transform, Elzaki transform, Sumudu transform, Mahgoub transform, Mohand transform and Sawi transform) are discussed and integral transforms of some typical functions are given in table form in application section to signify the fruitfulness of connections between Aboodh transform and some effective mention integral transforms.

scholarly journals A high-speed algorithm for computation of fractional differentiation and fractional integration

2013 ◽  
Vol 371 (1990) ◽  
pp. 20120152 ◽  
Author(s):  
Masataka Fukunaga ◽  
Nobuyuki Shimizu
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
High Speed ◽  
Fractional Integration ◽  
Computing Time ◽  
Fractional Differentiation ◽  
Time Step ◽  
Weighted Integrals ◽  
Fractional Differential

A high-speed algorithm for computing fractional differentiations and fractional integrations in fractional differential equations is proposed. In this algorithm, the stored data are not the function to be differentiated or integrated but the weighted integrals of the function. The intervals of integration for the memory can be increased without loss of accuracy as the computing time-step n increases. The computing cost varies as , as opposed to n 2 of standard algorithms.

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