scholarly journals More Properties of Fractional Proportional Differences

2021 ◽  
Vol 2 (1) ◽  
pp. 72-90
Author(s):  
Thabet Abdeljawad ◽  
Iyad Suwan ◽  
Fahd Jarad ◽  
Ammar Qarariyah
Keyword(s):  
Laplace Transform ◽  
Time Scale ◽  
Convolution Theorem ◽  
Fractional Operators

The main aim of this paper is to clarify the action of the discrete Laplace transform on the fractional proportional operators. First of all, we recall the nabla fractional sums and differences and the discrete Laplace transform on a time scale equivalent to $h\mathbb{Z}$. The discrete $h-$Laplace transform and its convolution theorem are then used to study the introduced discrete fractional operators.

scholarly journals ON THE WEIGHTED FRACTIONAL OPERATORS OF A FUNCTION WITH RESPECT TO ANOTHER FUNCTION

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040011 ◽  
Author(s):  
F. JARAD ◽  
T. ABDELJAWAD ◽  
K. SHAH
Keyword(s):  
Laplace Transform ◽  
Fractional Derivatives ◽  
Fractional Operators ◽  
Weighted Integrals

The primary goal of this study is to define the weighted fractional operators on some spaces. We first prove that the weighted integrals are bounded in certain spaces. Afterwards, we discuss the weighted fractional derivatives defined on absolute continuous-like spaces. At the end, we present a modified Laplace transform that can be applied perfectly to such operators.

THE GENERALIZED CONVOLUTION FOR h-LAPLACE TRANSFORM ON TIME SCALE

2019 ◽  
Vol 64 (10) ◽  
pp. 17-35
Author(s):  
Thao Nguyen Xuan ◽  
Tung Hoang
Keyword(s):  
Laplace Transform ◽  
Time Scale ◽  
Generalized Convolution

scholarly journals Gupta Transform Approach to the Series RL and RC Networks with Steady Excitation Sources

2021 ◽  
Vol 8 (2) ◽  
Author(s):  
Rahul Gupta ◽  
Rohit Gupta ◽  
Loveneesh Talwar
Keyword(s):  
Laplace Transform ◽  
Electric Current ◽  
Integral Transform ◽  
Complete Response ◽  
Convolution Theorem ◽  
Excitation Source ◽  
Voltage Source ◽  
Residue Theorem ◽  
Electric Networks ◽  
Rc Networks

The analysis of electric networks circuits is an essential course in engineering. The response of such networks is usually obtained by mathematical approaches such as Laplace Transform, Calculus Approach, Convolution Theorem Approach, Residue Theorem Approach. This paper presents a new integral transform called Gupta Transform for obtaining the complete response of the series RL and RC networks circuits with a steady voltage source. The response obtained will provide electric current or charge flowing through series RL and RC networks circuits with a steady voltage source. In this paper, the response of the series RL and RC networks circuits with steady excitation source is provided as a demonstration of the application of the new integral transform called Gupta Transform.

scholarly journals Fractional Operators Associated with the ք -Extended Mathieu Series by Using Laplace Transform

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Hafte Amsalu Kahsay ◽  
Adnan Khan ◽  
Sajjad Khan ◽  
Kahsay Godifey Wubneh
Keyword(s):  
Integral Operator ◽  
Laplace Transform ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Fractional Operators ◽  
The Laplace Transform ◽  
Mathieu Series

In this paper, our leading objective is to relate the fractional integral operator known as P δ -transform with the ք -extended Mathieu series. We show that the P δ -transform turns to the classical Laplace transform; then, we get the integral relating the Laplace transform stated in corollaries. As corollaries and consequences, many interesting outcomes are exposed to follow from our main results. Also, in this paper, we have converted the P δ -transform into a classical Laplace transform by changing the variable ln δ − 1 s + 1 / δ − 1 ⟶ s ; then, we get the integral involving the Laplace transform.

scholarly journals A New Dynamic Scheme via Fractional Operators on Time Scale

2020 ◽  
Vol 8 ◽  
Author(s):  
Saima Rashid ◽  
Muhammad Aslam Noor ◽  
Kottakkaran Sooppy Nisar ◽  
Dumitru Baleanu ◽  
Gauhar Rahman
Keyword(s):  
Time Scale ◽  
Fractional Operators

scholarly journals The Convolution on Time Scales

2007 ◽  
Vol 2007 ◽  
pp. 1-24 ◽  
Author(s):  
Martin Bohner ◽  
Gusein Sh. Guseinov
Keyword(s):  
Power Series ◽  
Transport Equation ◽  
Time Scales ◽  
Difference Equations ◽  
Initial Value Problem ◽  
Time Scale ◽  
Convolution Theorem ◽  
Main Theme ◽  
Initial Value ◽  
Dynamic Version

The main theme in this paper is an initial value problem containing a dynamic version of the transport equation. Via this problem, the delay (or shift) of a function defined on a time scale is introduced, and the delay in turn is used to introduce the convolution of two functions defined on the time scale. In this paper, we give some elementary properties of the delay and of the convolution and we also prove the convolution theorem. Our investigation contains a study of the initial value problem under consideration as well as some results about power series on time scales. As an extensive example, we consider theq-difference equations case.

scholarly journals Local Fractional Laplace Variational Iteration Method for Solving Diffusion and Wave Equations on Cantor Sets within Local Fractional Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Hassan Kamil Jassim ◽  
Canan Ünlü ◽  
Seithuti Philemon Moshokoa ◽  
Chaudry Masood Khalique
Keyword(s):  
Laplace Transform ◽  
Iteration Method ◽  
Wave Equations ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
High Accuracy ◽  
Cantor Set ◽  
Cantor Sets ◽  
Fractional Operators ◽  
Variational Iteration

The local fractional Laplace variational iteration method (LFLVIM) is employed to handle the diffusion and wave equations on Cantor set. The operators are taken in the local sense. The nondifferentiable approximate solutions are obtained by using the local fractional Laplace variational iteration method, which is the coupling method of local fractional variational iteration method and Laplace transform. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new algorithm.

scholarly journals On Weighted (k, s)-Riemann-Liouville Fractional Operators and Solution of Fractional Kinetic Equation

2021 ◽  
Vol 5 (3) ◽  
pp. 118
Author(s):  
Muhammad Samraiz ◽  
Muhammad Umer ◽  
Artion Kashuri ◽  
Thabet Abdeljawad ◽  
Sajid Iqbal ◽  
...  
Keyword(s):  
Kinetic Equation ◽  
Laplace Transform ◽  
Fractional Integral ◽  
Differential Operators ◽  
Laplace Transforms ◽  
The Novel ◽  
Fractional Operators ◽  
Fractional Kinetic Equation

In this article, we establish the weighted (k,s)-Riemann-Liouville fractional integral and differential operators. Some certain properties of the operators and the weighted generalized Laplace transform of the new operators are part of the paper. The article consists of Chebyshev-type inequalities involving a weighted fractional integral. We propose an integro-differential kinetic equation using the novel fractional operators and find its solution by applying weighted generalized Laplace transforms.

scholarly journals On Multiple Convolutions and Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Hassan Eltayeb ◽  
Adem Kılıçman ◽  
Brian Fisher
Keyword(s):  
Laplace Transform ◽  
Time Scales ◽  
Time Scale ◽  
Double Laplace Transform

The properties of the multiple Laplace transform and convolutions on a time scale are studied. Further, some related results are also obtained by utilizing the double Laplace transform. We also provide an example in order to illustrate the main result.

scholarly journals Integral Transform Methods for Solving Fractional Dynamic Equations on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Mohamad Rafi Segi Rahmat
Keyword(s):  
Laplace Transform ◽  
Time Scales ◽  
Time Scale ◽  
Integral Transform ◽  
Integral Transforms ◽  
Dynamic Equations ◽  
Transform Methods ◽  
Sumudu Transform ◽  
General Time

We introduce nabla type Laplace transform and Sumudu transform on general time scale. We investigate the properties and the applicability of these integral transforms and their efficiency in solving fractional dynamic equations on time scales.

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