Abstract and Applied Analysis

Recent Developments in Integral Transforms, Special Functions, and Their Extensions to Distributions Theory


Publishing date
19 Jul 2013
Status
Published
Submission deadline
01 Mar 2013

Lead Editor

1Yildiz Technical University, 34250 Istanbul, Turkey

2Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia


Recent Developments in Integral Transforms, Special Functions, and Their Extensions to Distributions Theory

Description

In recent years, there has been a growing interest in setting up a modeling and solving mathematical problems in order to explain numerous experimental findings which are relevant to industrial applications.

Distributions are also known as generalized functions which generalize the idea of classical functions and allow us to extend the concept of derivative to all continuous functions. The theory of distributions has applications in various fields especially in science and engineering where there are many noncontinuous phenomena that naturally lead to differential equations whose solutions are distributions, such as the delta distribution, and, therefore, distributions can help us to develop an operational calculus in order to investigate linear ordinary differential equations as well as partial differential equations with constant and variable coefficients through their fundamental solutions.

Considering some regular operations which are valid for ordinary functions such as addition, multiplication by scalars can be extended into distributions. Other operations can only be defined for certain restricted subclasses; these are called irregular operations. However, generalized functions are useful tools to extend the concept of derivative to all continuous functions and are further used to formulate generalized solutions of partial differential equations. They are important in physics and engineering where many noncontinuous problems naturally lead to differential equations whose solutions are distributions, such as the Dirac delta distribution.

This special issue will focus on the irregular operations with integrals transform, special functions, and their applications with fractional orders. A further relationship between linear and nonlinear partial differential equations and generalized functions is considered. Potential topics include, but are not limited to:

  • Integral transforms and their extension to distributions
  • Special functions and solutions to the fractional differential equations
  • Radon transform and its applications in CT scan
  • Financial modeling and role of generalized functions

Before submission authors should carefully read over the journal's Author Guidelines, which are located at http://www.hindawi.com/journals/aaa/guidelines/. Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at http://mts.hindawi.com/author/submit/journals/aaa/rdit/ according to the following timetable:


Articles

  • Special Issue
  • - Volume 2013
  • - Article ID 187383
  • - Research Article

A Numerical Solution to Fractional Diffusion Equation for Force-Free Case

O. Tasbozan | A. Esen | ... | Y. Ucar
  • Special Issue
  • - Volume 2013
  • - Article ID 750524
  • - Research Article

Unified Treatment of the Krätzel Transformation for Generalized Functions

S. K. Q. Al-Omari | A. Kılıçman
  • Special Issue
  • - Volume 2013
  • - Article ID 275915
  • - Research Article

On the Stability of Trigonometric Functional Equations in Distributions and Hyperfunctions

Jaeyoung Chung | Jeongwook Chang
  • Special Issue
  • - Volume 2013
  • - Article ID 348701
  • - Research Article

Some Remarks on the Extended Hartley-Hilbert and Fourier-Hilbert Transforms of Boehmians

S. K. Q. Al-Omari | A. Kılıçman
  • Special Issue
  • - Volume 2013
  • - Article ID 239454
  • - Research Article

A New Application of the Reproducing Kernel Hilbert Space Method to Solve MHD Jeffery-Hamel Flows Problem in Nonparallel Walls

Mustafa Inc | Ali Akgül | Adem Kılıçman
  • Special Issue
  • - Volume 2013
  • - Article ID 128458
  • - Research Article

On an Extension of Kummer's Second Theorem

Medhat A. Rakha | Mohamed M. Awad | Arjun K. Rathie
  • Special Issue
  • - Volume 2013
  • - Article ID 535979
  • - Research Article

Robustness of Operational Matrices of Differentiation for Solving State-Space Analysis and Optimal Control Problems

Emran Tohidi | F. Soleymani | Adem Kilicman
  • Special Issue
  • - Volume 2013
  • - Article ID 279681
  • - Research Article

A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions

Abdon Atangana | Aydin Secer
  • Special Issue
  • - Volume 2013
  • - Article ID 671321
  • - Research Article

A Generalized Version of a Low Velocity Impact between a Rigid Sphere and a Transversely Isotropic Strain-Hardening Plate Supported by a Rigid Substrate Using the Concept of Noninteger Derivatives

Abdon Atangana | O. Aden Ahmed | Necdet Bıldık
  • Special Issue
  • - Volume 2013
  • - Article ID 705313
  • - Research Article

A Numerical Method for Partial Differential Algebraic Equations Based on Differential Transform Method

Murat Osmanoglu | Mustafa Bayram
Abstract and Applied Analysis
 Journal metrics
Acceptance rate14%
Submission to final decision40 days
Acceptance to publication54 days
CiteScore1.300
Impact Factor-
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