Fractional Calculus and Nonlinear Analysis: Theory and Applications

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "General Mathematics, Analysis".

Deadline for manuscript submissions: 15 July 2024 | Viewed by 4300

Special Issue Editors


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Guest Editor
Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan
Interests: nonlinear analysis and its applications; fixed point theory; variational principles and inequalities; optimization theory; equilibrium problems; fractional calculus theory
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Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, Serbia
Interests: abstract Volterra integro-differential equations; abstract fractional differential equations; topological dynamics of linear operators and abstract PDEs
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
Department for Mathematics and Informatics, Faculty of Civil Engineering, Ss. Cyril and Methodius University in Skopje, Partizanski Odredi 24, P.O. Box 560, 1000 Skopje, North Macedonia
Interests: functional analysis; fractional calculus theory; generalized functions; semigroup theory; PDEs

Special Issue Information

Dear Colleagues,

Fractional calculus is a generalization of classical calculus that involves the study of non-integer derivatives and integrals and their applications. In recent decades, fractional calculus has been widely investigated and applied in various scientific fields such as probability and statistics, physical chemistry, electromagnetic theory, electronic networks, financial economics, biological engineering and so on. It is safe to say that almost all modern engineering and scientific disciplines have been influenced by the theory of fractional calculus, so many scholars have devoted themselves to the study of fractional calculus theory and achieved fruitful research results. Nonlinear analysis is one of the core areas of pure mathematics and applied mathematics. Over the centuries, it has been widely and significantly applied in many areas of mathematics, including critical point theory, functional analysis, fixed point theory, nonlinear ordinary and partial differential equations, nonlinear optimization, variational analysis, convex analysis, dynamical system theory, mathematical economics, signal processing, control theory, data mining, and so forth.

This Special Issue will pay more attention to the new originality and real-world applications of fractional calculus and nonlinear analysis. We cordially and earnestly invite researchers to contribute their original and high-quality research papers that will inspire advances in fractional calculus, nonlinear analysis and their applications. Potential topics include but are not limited to:

  • Boundary value problems of fractional differential equations;
  • Singular and impulsive fractional differential and integral equations;
  • Fractional complicated systems;
  • Fractional operators and their applications;
  • Modeling biological phenomena;
  • Non-locality in epidemic models and memory effects;
  • Nonlinear functional analysis;
  • Nonlinear dynamics and chaos;
  • Fixed-point theory and its applications;
  • Critical point theory;
  • Optimization;
  • Convex analysis.

Prof. Dr. Wei-Shih Du
Prof. Dr. Marko Kostić
Prof. Dr. Daniel Velinov
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fractional differential equation
  • fractional complicated system
  • fractional operator
  • modeling biological phenomena
  • nonlinear dynamics and chaos
  • fixed point theory
  • optimization
  • critical point theory
  • optimization
  • convex analysis

Published Papers (4 papers)

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Research

10 pages, 265 KiB  
Article
Existence Results Related to a Singular Fractional Double-Phase Problem in the Whole Space
by Ramzi Alsaedi
Fractal Fract. 2024, 8(5), 292; https://doi.org/10.3390/fractalfract8050292 - 16 May 2024
Viewed by 207
Abstract
In this paper, we will study a singular problem involving the fractional (q1(x,.)-q2(x,.))-Laplacian operator in the whole space RN,(N2) [...] Read more.
In this paper, we will study a singular problem involving the fractional (q1(x,.)-q2(x,.))-Laplacian operator in the whole space RN,(N2). More precisely, we combine the variational method with monotonicity arguments to prove that the associated functional energy admits a critical point, which is a weak solution for such a problem. Full article
(This article belongs to the Special Issue Fractional Calculus and Nonlinear Analysis: Theory and Applications)
28 pages, 481 KiB  
Article
Stepanov Almost Periodic Type Functions and Applications to Abstract Impulsive Volterra Integro-Differential Inclusions
by Marko Kostić and Wei-Shih Du
Fractal Fract. 2023, 7(10), 736; https://doi.org/10.3390/fractalfract7100736 - 6 Oct 2023
Viewed by 771
Abstract
In this paper, we analyze various classes of Stepanov-p-almost periodic functions and Stepanov-p-almost automorphic functions (p>0). The class of Stepanov-p-almost periodic (automorphic) functions in norm (p>0) is also introduced [...] Read more.
In this paper, we analyze various classes of Stepanov-p-almost periodic functions and Stepanov-p-almost automorphic functions (p>0). The class of Stepanov-p-almost periodic (automorphic) functions in norm (p>0) is also introduced and analyzed. Some structural results for the introduced classes of functions are clarified. We also provide several important theoretical examples, useful remarks and some new applications of Stepanov-p-almost periodic type functions to the abstract (impulsive) first-order differential inclusions and the abstract (impulsive) fractional differential inclusions. Full article
(This article belongs to the Special Issue Fractional Calculus and Nonlinear Analysis: Theory and Applications)
21 pages, 776 KiB  
Article
Qualitative and Quantitative Analysis of Fractional Dynamics of Infectious Diseases with Control Measures
by Sultan Alyobi and Rashid Jan
Fractal Fract. 2023, 7(5), 400; https://doi.org/10.3390/fractalfract7050400 - 15 May 2023
Cited by 5 | Viewed by 1135
Abstract
Infectious diseases can have a significant economic impact, both in terms of healthcare costs and lost productivity. This can be particularly significant in developing countries, where infectious diseases are more prevalent, and healthcare systems may be less equipped to handle them. It is [...] Read more.
Infectious diseases can have a significant economic impact, both in terms of healthcare costs and lost productivity. This can be particularly significant in developing countries, where infectious diseases are more prevalent, and healthcare systems may be less equipped to handle them. It is recognized that the hepatitis B virus (HBV) infection remains a critical global public health issue. In this study, we develop a comprehensive model for HBV infection that includes vaccination and hospitalization through a fractional framework. It has been shown that the solutions of the recommended system of HBV infection are positive and bounded. We examine the steady states of the model and determine the basic reproduction number; denoted by R0. The qualitative and quantitative behavior of the model is demonstrated using mathematical skills and numerical techniques. It has been proved that the infection-free steady state of the system is locally asymptotically stable if R0<1 and unstable otherwise. Furthermore, the Ulam–Hyers stability (UHS) of the recommended fractional models is investigated and the significant conditions are provided. We present an iterative technique to visualize the dynamical behavior of the system. We perform different simulations to illustrate the effect of different input factors on the solution pathways of the system of HBV infection to conceptualize the role of parameters in the control and prevention of the infection. Full article
(This article belongs to the Special Issue Fractional Calculus and Nonlinear Analysis: Theory and Applications)
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15 pages, 412 KiB  
Article
A Sufficient and Necessary Condition for the Power-Exponential Function 1+1xαx to Be a Bernstein Function and Related nth Derivatives
by Jian Cao, Bai-Ni Guo, Wei-Shih Du and Feng Qi
Fractal Fract. 2023, 7(5), 397; https://doi.org/10.3390/fractalfract7050397 - 13 May 2023
Viewed by 1227
Abstract
In the paper, the authors find a sufficient and necessary condition for the power-exponential function 1+1xαx to be a Bernstein function, derive closed-form formulas for the nth derivatives of the power-exponential functions [...] Read more.
In the paper, the authors find a sufficient and necessary condition for the power-exponential function 1+1xαx to be a Bernstein function, derive closed-form formulas for the nth derivatives of the power-exponential functions 1+1xαx and (1+x)α/x, and present a closed-form formula of the partial Bell polynomials Bn,k(H0(x),H1(x),,Hnk(x)) for nk0, where Hk(x)=0eu1ueuuk1exudu for k0 are completely monotonic on (0,). Full article
(This article belongs to the Special Issue Fractional Calculus and Nonlinear Analysis: Theory and Applications)
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