Differentiation Property of Fractional Hankel Transform of a Function Involving Higher Order Derivatives

In engineering mathematics, integral transform is a widely used tool for solving linear differential equations, In recent  times  the newly born  fractional Hankel  transform has been started for   playing a very important    role  in various  fields of applied  mathematics and physics like fractional Fourier transform. This paper represent   a formalization of differentiation property of a function invoving  high order derivatives  of  newly introduced     fractional Hankel  transform. The differentiation property is  proved for different higher differential equations

N-dimensional Fractional Fourier Transform and its Eigenvalues and Eigenfunctions

In this paper, we have  established the N- dimentional fractional Fourier transform and its mathematical expression in a easier manner and discus the  eigenvalues and eigenfunctions of   -dimensional fractional Fourier transform

On the Relationship Between the Fractional Sumudu Transform and Fractional Fourier Transform

In this paper we have discussed fractional Sumudu transforms and its relationship with fractional Fourier transform and obtained the mathematical expression of kernel of fractional Sumudu transform. Such findings  will play a significant role for fractional Sumudu transform to recognize its importance in the  fields of engineering and applied mathematics  like other fractional transforms

On the Uniquness of Solutions of Linear Ordinary Fractional Differential Equations by Using Different Integral Transform Methods

The main objective of this paper has to investigate the uniqueness of the solution of fractional differential equation by using different integral transforms, we applied Laplace transform, Elzaki transform and Sumudu transform on a linear ordinary fractional differential equation. The uniqueness of the solution is achieved in fractional differential equations by applying different integral transform methods

Preliminary Neo-Deterministic Seismic Hazard Assessment in Pakistan and Adjoining Regions

The regional seismic hazard in Pakistan and adjoining regions is assessed using the Neo-deterministic seismic hazard assessment approach (NDSHA). Synthetic seismograms are generated by the modal summation technique at the nodes of a grid that covers the studied area. The main input for the computations consists of a set of earthquake sources and of the structural model where the seismic waves propagate. The earthquake sources are parameterised within the active seismogenic areas by defining the focal mechanism, the depth and the magnitude, obtained through the analysis and re- elaboration of the past seismicity. The peak displacement (Dmax), peak velocity (Vmax) and design ground acceleration (DGA) are then extracted from the synthetic signals and plotted on the 0.2\ub0 x 0.2\ub0 grid to construct the seismic hazard map of the studied area. There are few probabilistic hazard maps available for Pakistan, however, this is the first study aimed at producing a neo-deterministic seismic hazard map for Pakistan and adjoining regions.The most severe hazard is found in the epicentral zone of the great Muzaffarabad earthquakes of 2005 and its surroundings, where the DGA estimate falls in the highest range 0.60 g \u2013 1.2 g. The peak velocity and displacement in the same region are estimated as 60 12120 cm s 121 and 30 1260 cm, respectively

Fractional Radon Transform and its Convolution Theorem

Fractional Radon transform which is symbolized with the notation , it is different to the classical Radon transform. The shift property of fractional Radon transform is controlled by the fractional order Rotation of the input object at angle  will rotate the fractional Radon transform at that angle thus, the fractional Radon transform is rotation invariant. The fractional Fourier transform, with respect to  of the fractional Radon transform of an object is the central slice at angle  of the -dimensional fractional Fourier transform of this object. In this paper we explain the mathematical formation of fractional Radon transform and established a convolution theorem for the fractional Radon transform

How Fractional Charge on an Electron in the Momentum Space is Quantized?

With our conjecture on charge quantization (quantum dipole moment in a momentum space) and using Fractional Fourier Transform (FRFT) analysis on Hermite Polynomials (usually used for quantum oscillators), we obtained energy profiles (eigenfunctions) for fractional quantum states on the continuously changing surface of the electron. The charge on an electron as a physical constant and a single entity is degenerate because it always resides on the surface. The charge is fractionally quantized in momentum space. The continuous charging surface of the electron is due to competition between the centrifugal and electodynamic potentials. The fractional quantized states of charges in the momentum space are the manifestations of gyroscopic constants,   twisting and twigging of energy profiles (quantum electrodynamic behavior), oscillatory behavior of energy associated with degeneracy and indeed the position of fractional quanta in terms of rotational vector,  in complex plane.

The Relationship of Fractional Laplace Transform with Fractional Fourier, Mellin and Sumudu Transforms

We have developed in this research paper, some of the fundamental relationship of fractional Laplace transform with fractional Fourier, fractional Mellin and fractional Sumudu transforms. These results are expressed mathematically, and such relationships should be very useful in applications to signal processing and optics

The Relationship of Generalized Fractional Hilbert Transform with Fractional Mellin and Fractional Laplace Transforms

We have developed in this research paper, some of the fundamental relationship between generalized fractional Hilbert transform with fractional Mellin transform, fractional Laplace transform, fractional inverse Laplace transform.. The results are mathematically expressed. These results, however, need modelling and simulation with any specialized signal processing data

An Aperiodic Stable Chaos with Lyapunov Exponents in Time Series

A new formula is developed to reproduce the shape of energy profiles for aperiodic stable attractors with Lyapunov exponents,   by using the Fractional Fourier Transform (FRFT), .i.e.  where,  is the initial angular frequency of the of the attractor and  , the time of flight of the attractor. With, the energy profile for periodic unstable attractors at different values of Lyapunov exponents is obtained, for   aperiodic stable attraction at different values of Lyapunov exponents are observed.  The critical analysis about chaos is presented with emphasis to time series modeling and simulation