Table of Content

Recent Advances in Fractional Calculus Applied to Complex Engineering Phenomena

Submission Deadline: 31 May 2021 (closed)

Guest Editors

Prof. Dumitru Baleanu, Cankaya University, Romania.
Dr. Sunil Kumar, National Institute of Technology, India.
Prof. Carlo Cattani, Tuscia University, Italy.
Dr. Carla M. A. Pinto, School of Engineering of the Polytechnic of Porto, Portugal.


In the past few decades, fractional derivatives have been recognized as powerful modelling and simulation tools for mechanical engineering problems. Many physical laws are expressed more accurately in terms of differential equations of arbitrary order.  In this Special Issue, we kindly invite researchers to present their original work in the area of fractional differential equations as models of complex engineering problems. These works may bring new theories, development of numerical methods, and applications. All research articles should fit the scope of the journal Computers, Materials & Continua, and topics of interests include (but are not limited to):

· Mathematical modelling of complex engineering problems using fractional differential


· Artificial intelligence and data analysis within fractional calculus methods and techniques

· Advanced analytical and numerical methods for fractional differential equations

· Real world applications of fractional models in engineering

· Mathematical modeling of engineering fractional dynamic systems

· Computational and numerical methodologies for fractional differential equations with engineering meaning


Fractional dynamics;Fractional modelling of complex engineering problems; Non-local analytical and numerical methods;Artificial intelligence;Data analysis.

Published Papers

  • Open Access


    Image Splicing Detection Based on Texture Features with Fractal Entropy

    Razi J. Al-Azawi, Nadia M. G. Al-Saidi, Hamid A. Jalab, Rabha W. Ibrahim, Dumitru Baleanu
    CMC-Computers, Materials & Continua, Vol.69, No.3, pp. 3903-3915, 2021, DOI:10.32604/cmc.2021.020368
    (This article belongs to this Special Issue: Recent Advances in Fractional Calculus Applied to Complex Engineering Phenomena)
    Abstract Over the past years, image manipulation tools have become widely accessible and easier to use, which made the issue of image tampering far more severe. As a direct result to the development of sophisticated image-editing applications, it has become near impossible to recognize tampered images with naked eyes. Thus, to overcome this issue, computer techniques and algorithms have been developed to help with the identification of tampered images. Research on detection of tampered images still carries great challenges. In the present study, we particularly focus on image splicing forgery, a type of manipulation where a region of an image is… More >

  • Open Access


    A Fractional Drift Diffusion Model for Organic Semiconductor Devices

    Yi Yang, Robert A. Nawrocki, Richard M. Voyles, Haiyan H. Zhang
    CMC-Computers, Materials & Continua, Vol.69, No.1, pp. 237-266, 2021, DOI:10.32604/cmc.2021.017439
    (This article belongs to this Special Issue: Recent Advances in Fractional Calculus Applied to Complex Engineering Phenomena)
    Abstract Because charge carriers of many organic semiconductors (OSCs) exhibit fractional drift diffusion (Fr-DD) transport properties, the need to develop a Fr-DD model solver becomes more apparent. However, the current research on solving the governing equations of the Fr-DD model is practically nonexistent. In this paper, an iterative solver with high precision is developed to solve both the transient and steady-state Fr-DD model for organic semiconductor devices. The Fr-DD model is composed of two fractional-order carriers (i.e., electrons and holes) continuity equations coupled with Poisson’s equation. By treating the current density as constants within each pair of consecutive grid nodes, a… More >

  • Open Access


    The Investigation of the Fractional-View Dynamics of Helmholtz Equations Within Caputo Operator

    Rashid Jan, Hassan Khan, Poom Kumam, Fairouz Tchier, Rasool Shah, Haifa Bin Jebreen
    CMC-Computers, Materials & Continua, Vol.68, No.3, pp. 3185-3201, 2021, DOI:10.32604/cmc.2021.015252
    (This article belongs to this Special Issue: Recent Advances in Fractional Calculus Applied to Complex Engineering Phenomena)
    Abstract It is eminent that partial differential equations are extensively meaningful in physics, mathematics and engineering. Natural phenomena are formulated with partial differential equations and are solved analytically or numerically to interrogate the system’s dynamical behavior. In the present research, mathematical modeling is extended and the modeling solutions Helmholtz equations are discussed in the fractional view of derivatives. First, the Helmholtz equations are presented in Caputo’s fractional derivative. Then Natural transformation, along with the decomposition method, is used to attain the series form solutions of the suggested problems. For justification of the proposed technique, it is applied to several numerical examples.… More >

  • Open Access


    A New Medical Image Enhancement Algorithm Based on Fractional Calculus

    Hamid A. Jalab, Rabha W. Ibrahim, Ali M. Hasan, Faten Khalid Karim, Ala’a R. Al-Shamasneh, Dumitru Baleanu
    CMC-Computers, Materials & Continua, Vol.68, No.2, pp. 1467-1483, 2021, DOI:10.32604/cmc.2021.016047
    (This article belongs to this Special Issue: Recent Advances in Fractional Calculus Applied to Complex Engineering Phenomena)
    Abstract The enhancement of medical images is a challenging research task due to the unforeseeable variation in the quality of the captured images. The captured images may present with low contrast and low visibility, which might influence the accuracy of the diagnosis process. To overcome this problem, this paper presents a new fractional integral entropy (FITE) that estimates the unforeseeable probabilities of image pixels, posing as the main contribution of the paper. The proposed model dynamically enhances the image based on the image contents. The main advantage of FITE lies in its capability to enhance the low contrast intensities through pixels’… More >

  • Open Access


    Fractional-Order Control of a Wind Turbine Using Manta Ray Foraging Optimization

    Hegazy Rezk, Mohammed Mazen Alhato, Mohemmed Alhaider, Soufiene Bouallègue
    CMC-Computers, Materials & Continua, Vol.68, No.1, pp. 185-199, 2021, DOI:10.32604/cmc.2021.016175
    (This article belongs to this Special Issue: Recent Advances in Fractional Calculus Applied to Complex Engineering Phenomena)
    Abstract In this research paper, an improved strategy to enhance the performance of the DC-link voltage loop regulation in a Doubly Fed Induction Generator (DFIG) based wind energy system has been proposed. The proposed strategy used the robust Fractional-Order (FO) Proportional-Integral (PI) control technique. The FOPI control contains a non-integer order which is preferred over the integer-order control owing to its benefits. It offers extra flexibility in design and demonstrates superior outcomes such as high robustness and effectiveness. The optimal gains of the FOPI controller have been determined using a recent Manta Ray Foraging Optimization (MRFO) algorithm. During the optimization process,… More >

  • Open Access


    Fractional Rényi Entropy Image Enhancement for Deep Segmentation of Kidney MRI

    Hamid A. Jalab, Ala’a R. Al-Shamasneh, Hadil Shaiba, Rabha W. Ibrahim, Dumitru Baleanu
    CMC-Computers, Materials & Continua, Vol.67, No.2, pp. 2061-2075, 2021, DOI:10.32604/cmc.2021.015170
    (This article belongs to this Special Issue: Recent Advances in Fractional Calculus Applied to Complex Engineering Phenomena)
    Abstract Recently, many rapid developments in digital medical imaging have made further contributions to health care systems. The segmentation of regions of interest in medical images plays a vital role in assisting doctors with their medical diagnoses. Many factors like image contrast and quality affect the result of image segmentation. Due to that, image contrast remains a challenging problem for image segmentation. This study presents a new image enhancement model based on fractional Rényi entropy for the segmentation of kidney MRI scans. The proposed work consists of two stages: enhancement by fractional Rényi entropy, and MRI Kidney deep segmentation. The proposed… More >

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