Special lssues
Table of Content

On Innovative Ideas in Pure and Applied Mathematics with Applications

Submission Deadline: 15 March 2023 (closed)

Guest Editors

Prof. Ahmet Ocak Akdemir, Ağrı İbrahim Çeçen University, Turkey
Prof. Maria Alessandra Ragusa, Università di Catania, Italy
Prof. Mustafa Ali Dokuyucu, Ağrı İbrahim Çeçen University, Turkey


Mathematics is a useful tool that explains physical phenomena, provides a working platform for applied and computational sciences, and establishes relationships between well-known concepts in fields such as statistics, finance, programming and biology. When mathematical concepts are evaluated together with the corresponding phenomena in applied sciences, a solution-oriented approach emerges by giving modeling and simulations to real-world problems. The importance of a true mathematical concept or method lies in the extent to which it serves this solution-oriented approach. The functionality of a differential or integral equation is measured by its contribution to the solution of the real-world problem it represents.

Derivative and integral operators, which are used as tools to understand the working principles of dynamic systems, form the basis of mathematical modeling. The fact that it is so important has led to deep studies on the subject, and it has led to the discovery of fractional operators, which are the general form of integer order operators. The most important difference from the classical derivative and integral is that it has more than one definition in order to obtain the best solution according to the type of problem. However, the fact that it has almost no practical application has caused it to be accepted as an abstract field that includes only mathematical operations. About half a century ago, the paradigm began to move from pure mathematical formulations to applications in various fields, and in the last 20 years fractional operators have entered almost every field of science, engineering and mathematics.

This special issue is to provide an interdisciplinary forum of discussion in different fields of mathematics and statistics but also to physics, engineering, control theory, mathematical biology, chemistry, approximation theory, finance, nature and so on. This issue will be a collection of the high-quality papers. Subject matters should be related to fractional calculus, geometrical and algebraic structures, cryptosystems and applications to real world problems. The main purpose of this special issue is to focus the considerable of findings and methods of the innovative and trend topics in pure and applied mathematics.


Potential topics include but are not limited to the following:

· Disease models

· Fuzzy Fractional differential equations

· Discrete fractional calculus and applications

· Fractional differential equations

· Fractional derivatives and special functions

· Special functions related to fractional (non-integer) order control systems and equations

· Applications of fractional calculus in mechanics

· Applications of fractional calculus in physics

· Fractional diffusion-wave equation systems

· Fractional integral inequalities and their q-analogues

· Inequalities involving the fractional integral operators

· Cryptology

· Geometrical structures with ordinary and fractional operators

· Numerical solution methods and control theory

· Chaos theory

· Regularity of Minimizers for fractional Differential Equations

· Inclusions, inequalities and applications

· Stochastic Analysis and Modelling

· Approximation Theory with Applications


Disease models; fractional calculus; control theory; discrete systems; modelling of physical systems; regularity

Published Papers

  • Open Access


    Results Involving Partial Differential Equations and Their Solution by Certain Integral Transform

    Rania Saadah, Mohammed Amleh, Ahmad Qazza, Shrideh Al-Omari, Ahmet Ocak Akdemir
    CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.2, pp. 1593-1616, 2024, DOI:10.32604/cmes.2023.029180
    (This article belongs to this Special Issue: On Innovative Ideas in Pure and Applied Mathematics with Applications)
    Abstract In this study, we aim to investigate certain triple integral transform and its application to a class of partial differential equations. We discuss various properties of the new transform including inversion, linearity, existence, scaling and shifting, etc. Then, we derive several results enfolding partial derivatives and establish a multi-convolution theorem. Further, we apply the aforementioned transform to some classical functions and many types of partial differential equations involving heat equations, wave equations, Laplace equations, and Poisson equations as well. Moreover, we draw some figures to illustrate 3-D contour plots for exact solutions of some selected examples involving different values in… More >

  • Open Access


    A New Scheme of the ARA Transform for Solving Fractional-Order Waves-Like Equations Involving Variable Coefficients

    Yu-Ming Chu, Sobia Sultana, Shazia Karim, Saima Rashid, Mohammed Shaaf Alharthi
    CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.1, pp. 761-791, 2024, DOI:10.32604/cmes.2023.028600
    (This article belongs to this Special Issue: On Innovative Ideas in Pure and Applied Mathematics with Applications)
    Abstract The goal of this research is to develop a new, simplified analytical method known as the ARA-residue power series method for obtaining exact-approximate solutions employing Caputo type fractional partial differential equations (PDEs) with variable coefficient. ARA-transform is a robust and highly flexible generalization that unifies several existing transforms. The key concept behind this method is to create approximate series outcomes by implementing the ARA-transform and Taylor’s expansion. The process of finding approximations for dynamical fractional-order PDEs is challenging, but the ARA-residual power series technique magnifies this challenge by articulating the solution in a series pattern and then determining the series… More >

  • Open Access


    On Time Fractional Partial Differential Equations and Their Solution by Certain Formable Transform Decomposition Method

    Rania Saadeh, Ahmad Qazza, Aliaa Burqan, Shrideh Al-Omari
    CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 3121-3139, 2023, DOI:10.32604/cmes.2023.026313
    (This article belongs to this Special Issue: On Innovative Ideas in Pure and Applied Mathematics with Applications)
    Abstract This paper aims to investigate a new efficient method for solving time fractional partial differential equations. In this orientation, a reliable formable transform decomposition method has been designed and developed, which is a novel combination of the formable integral transform and the decomposition method. Basically, certain accurate solutions for time-fractional partial differential equations have been presented. The method under concern demands more simple calculations and fewer efforts compared to the existing methods. Besides, the posed formable transform decomposition method has been utilized to yield a series solution for given fractional partial differential equations. Moreover, several interesting formulas relevant to the… More >

  • Open Access


    Notes on Curves at a Constant Distance from the Edge of Regression on a Curve in Galilean 3-Space

    Ali Çakmak, Sezai Kızıltuğ, Gökhan Mumcu
    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2731-2742, 2023, DOI:10.32604/cmes.2023.024517
    (This article belongs to this Special Issue: On Innovative Ideas in Pure and Applied Mathematics with Applications)
    Abstract In this paper, we define the curve at a constant distance from the edge of regression on a curve r(s) with arc length parameter s in Galilean 3-space. Here, d is a non-isotropic or isotropic vector defined as a vector tightly fastened to Frenet trihedron of the curve r(s) in 3-dimensional Galilean space. We build the Frenet frame of the constructed curve with respect to two types of the vector d and we indicate the properties related to the curvatures of the curve . Also, for the curve , we give the conditions to be a circular helix. Furthermore, we… More >

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