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 379856
  • - Editorial

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

Adem Kılıçman | Mustafa Bayram | Hassan Eltayeb
  • Special Issue
  • - Volume 2013
  • - Article ID 435030
  • - Research Article

A Proposal to the Solution of Multiobjective Linear Fractional Programming Problem

Nuran Güzel
  • Special Issue
  • - Volume 2013
  • - Article ID 357931
  • - Research Article

An Efficient Pseudospectral Method for Solving a Class of Nonlinear Optimal Control Problems

Emran Tohidi | Atena Pasban | ... | S. Lotfi Noghabi
  • Special Issue
  • - Volume 2013
  • - Article ID 750964
  • - Research Article

On a Kind of Dirichlet Character Sums

Rong Ma | Yulong Zhang | Guohe Zhang
  • Special Issue
  • - Volume 2013
  • - Article ID 632384
  • - Research Article

Lipschitz Estimates for Fractional Multilinear Singular Integral on Variable Exponent Lebesgue Spaces

Hui-Ling Wu | Jia-Cheng Lan
  • Special Issue
  • - Volume 2013
  • - Article ID 968464
  • - Research Article

Modeling of Thermal Distributions around a Barrier at the Interface of Coating and Substrate

Ali Sahin
  • Special Issue
  • - Volume 2013
  • - Article ID 768963
  • - Research Article

Numerical Solutions of the Second-Order One-Dimensional Telegraph Equation Based on Reproducing Kernel Hilbert Space Method

Mustafa Inc | Ali Akgül | Adem Kılıçman
  • Special Issue
  • - Volume 2013
  • - Article ID 381980
  • - Research Article

Data Dependence Results for Multistep and CR Iterative Schemes in the Class of Contractive-Like Operators

Vatan Karakaya | Faik Gürsoy | ... | Müzeyyen Ertürk
  • Special Issue
  • - Volume 2013
  • - Article ID 686483
  • - Research Article

Numerical Solution and Simulation of Second-Order Parabolic PDEs with Sinc-Galerkin Method Using Maple

Aydin Secer
  • Special Issue
  • - Volume 2013
  • - Article ID 865952
  • - Research Article

Computational Solution of a Fractional Integro-Differential Equation

Muhammet Kurulay | Mehmet Ali Akinlar | Ranis Ibragimov
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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