Applied and Computational Mathematics

Special Issue

Singular Integral Equations and Fractional Differential Equations

  • Submission Deadline: 30 November 2017
  • Status: Submission Closed
  • Lead Guest Editor: Babak Shiri
About This Special Issue
Integral algebraic equations, weakly singular integral equations, singular integral equations of Cauchy type are completely different branch of singular integral equations. However, the singularities of their kernels are their common difficulties and problems. The system of integral algebraic equations has singularity in an open interval of the real or the complex fields. The other types of singular integral equations have singularity in discrete sets. The Abel’s integral equations are important weakly type singular integral equations. They have been studied in last two centuries. The fractional integrals or derivatives are also weakly singular integrals. In the last three decade, fractional (partial) deferential equations have been received more attention and applications. It seems that the results of weakly singular integral equations can be applied in the fractional differential equations and vice versa. The kernel of Cauchy type singular integral equations also is similar to the kernel of weakly singular integral equations but it has completely different analysis and applications. The aim of this special issue is to consider these topics in one issue.

Aims and scopes:
(1) Integral-Algebraic Equations
(2) Weakly Singular Integral Equations
(3) Abel Integral Equations
(3) Singular Integral Equations of Cauchy Type
(4) Fractional Differential Equations
(5) Fractional Partial Differential Equations
Lead Guest Editor
  • Babak Shiri

    Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

Guest Editors
  • Mohammad Saidul Islam

    Science & Engineering Faculty, Queensland University of Technology, Brisbane, Australia

  • Ercan Çelik

    Department of Mathematics, Ataturk University, Erzurum, Turkey

  • Elham Sefidgar

    Applied Mathematics, Atatürk university, Erzurum, Turkey

  • Mehar Chand

    Department of Applied Sciences, Guru Kashi University, Bathinda, India

  • Zahra Moayyerizadeh

    Department of Mathematics, Lorestan University, Khorramabad, Iran

  • Mehdi Ahmadi

    Department of Mathematics, Malayer University, Malayer, Iran

  • Davoud Abdollahi

    Department of Applied Mathematics, University of Tabriz, Tabriz, Iran

  • Kholamreza Karamali

    Faculty of science, Islamic Azad University South Tehran Branch, Tehran, Iran

  • Hossein Fazli

    Department of Applied Mathematic, University of Tabriz, Tabriz, Iran

  • Mahnaz Kashfi

    Department of Applied Mathematics, University of Tabriz, Tabriz, Iran

  • Prof. Dr. Hamed Daei Kasmaei

    Department of Applied Mathematics and Computer Science, Islamic Azad University,Central Tehran Branch, Tehran, Iran, Tehran, Iran

Published Articles
  • A Convergence Analysis of Discontinuous Collocation Method for IAEs of Index 1 Using the Concept “Strongly Equivalent”

    Gholamreza Karamali , Babak Shiri , Elham Sefidgar

    Issue: Volume 7, Issue 1-1, January 2018
    Pages: 12-17
    Received: 30 April 2017
    Accepted: 2 May 2017
    Published: 13 May 2017
    DOI: 10.11648/j.acm.s.2018070101.12
    Abstract: We introduce the concept “strongly equivalent” for integral algebraic equations (IAEs). This definition and its corresponding theorems construct powerful tools for the classifying and analyzing of IAEs (especially numerical analysis). The related theorems with short proofs provide powerful techniques for the complete convergence analysis of discret... Show More
  • Convergence Analysis of Piecewise Polynomial Collocation Methods for System of Weakly Singular Volterra Integral Equations of The First Kind

    Gholamreza Karamali , Babak Shiri , Mahnaz Kashfi

    Issue: Volume 7, Issue 1-1, January 2018
    Pages: 1-11
    Received: 21 March 2017
    Accepted: 22 March 2017
    Published: 11 April 2017
    DOI: 10.11648/j.acm.s.2018070101.11
    Abstract: We study regularity of solutions of weakly singular Volterra integral equations of the first kind. We then study the numerical analysis of discontinuous piecewise polynomial collocation methods for solving such systems. The main purpose of this paper is the derivation of global convergent and super-convergent properties of introduced methods on the... Show More