Journal of Function Spaces

Fractional Differentiation and Integration: Above Power Law, Exponential Decay and the Generalized Mittag-Leffler Kernels


Publishing date
01 Feb 2022
Status
Closed
Submission deadline
08 Oct 2021

1King Saud University, Riyadh, Saudi Arabia

2Ambedkar University Delhi, Delhi, India

3Mugla Sıtkı Kocman University, Mugla, Turkey

This issue is now closed for submissions.
More articles will be published in the near future.

Fractional Differentiation and Integration: Above Power Law, Exponential Decay and the Generalized Mittag-Leffler Kernels

This issue is now closed for submissions.
More articles will be published in the near future.

Description

Fractional calculus is a rapidly growing area of research that has attracted attention in many academic fields due to its wide applicability. In the last few decades, it has been recognized as a powerful mathematical tool to model complex real-world problems. One of the strengths of these operators is their ability to replicate processes like the power law, exponential decay memory, and even a passage from fading memory to the power law. Indeed, a number of real-world problems follow the power law, while others follow fading memory and other crossovers.

Of course, with different types of kernels, different results should be expected in theory and applications. While researchers have reached a certain level of satisfaction due to the modeling results obtained from these differential and integral operators, it is worth noting that they have not fully been able to model all real-world problems. Several novel operators have been suggested recently – for example, the concept of fractal fractional differentiation and integration, which combines fractal derivative and fractional kernels via convolution. These operators have also proven to be very efficient in modeling real-world problems with nonlocal processes and self-similar processes. However, this concept is new and needs more theoretical results and applications in different academic fields. In addition, randomness has been observed in many real-world problems and stochastic differential operators and many other methods have been adopted to solve these problems. Nevertheless, there are many physical problems following processes including non-locality and random walk. These problems cannot be modeled using neither fractional derivatives nor stochastic approaches., By combining both concepts, some of these problems could be solved with great success. There is a great need to establish new theoretical results and apply such concepts to model real-world problems arising in many fields of science and technology.

This Special Issue will therefore be devoted to collecting results in the theory and application of global differential and integral operators, piecewise differential and integral operators, and stochastic fractional differential and integral operators. Original research and review articles are welcome.

Potential topics include but are not limited to the following:

  • Application of piecewise differential and integral equations to real world problems
  • Application of global differentiation and integration to modeling complex problems
  • Application of stochastic fractional differential and integral operators
  • Theoretical results of fractional stochastic ordinary differential equations with piece-wise operators
  • Theoretical results of global fractional stochastic partial differential equations
  • Application of stochastic fractional differential and integral equations to chaos
  • Application of piecewise differential and integral equations to epidemiology
  • Piecewise fractional stochastic delay differential equations
  • Delay equations with fractional global differential and integral operators
  • Application of fractional stochastic partial differential equations to complex real-world problems
  • Application of fractional stochastic delay partial differential and integral equations
  • Piece-wise nonlinear fractional stochastic differential and integral equations with applications

Articles

  • Special Issue
  • - Volume 2022
  • - Article ID 3771137
  • - Research Article

Stability Analysis and Optimal Control Strategies of Giving Up Relapse Smoking Model with Bilinear and Harmonic Mean Type of Incidence Rates

Badr Saad T. Alkahtani
  • Special Issue
  • - Volume 2022
  • - Article ID 5877970
  • - Research Article

A Fractional-Order Investigation of Vaccinated SARS-CoV-2 Epidemic Model with Caputo Fractional Derivative

Badr Saad T. Alkahtani
  • Special Issue
  • - Volume 2021
  • - Article ID 9358496
  • - Research Article

Mixture of Lindley and Lognormal Distributions: Properties, Estimation, and Application

A. S. Al-Moisheer
  • Special Issue
  • - Volume 2021
  • - Article ID 1148618
  • - Research Article

Modelling to Engineering Data Using a New Class of Continuous Models

I. Elbatal | Naif Alotaibi
  • Special Issue
  • - Volume 2021
  • - Article ID 5207152
  • - Research Article

Global Stability for Novel Complicated SIR Epidemic Models with the Nonlinear Recovery Rate and Transfer from Being Infectious to Being Susceptible to Analyze the Transmission of COVID-19

Fehaid Salem Alshammari | F. Talay Akyildiz
  • Special Issue
  • - Volume 2021
  • - Article ID 8331731
  • - Research Article

On Impulsive Boundary Value Problem with Riemann-Liouville Fractional Order Derivative

Zareen A. Khan | Rozi Gul | Kamal Shah
  • Special Issue
  • - Volume 2021
  • - Article ID 6069201
  • - Research Article

Further Developments of Bessel Functions via Conformable Calculus with Applications

Mahmoud Abul-Ez | Mohra Zayed | Ali Youssef
  • Special Issue
  • - Volume 2021
  • - Article ID 4797955
  • - Research Article

Analytic Normalized Solutions of 2D Fractional Saint-Venant Equations of a Complex Variable

Najla M. Alarifi | Rabha W. Ibrahim
  • Special Issue
  • - Volume 2021
  • - Article ID 3484482
  • - Research Article

Numerical Analysis of Fractional-Order Parabolic Equations via Elzaki Transform

Muhammad Naeem | Omar Fouad Azhar | ... | Rasool Shah
Journal of Function Spaces
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Article of the Year Award: Outstanding research contributions of 2021, as selected by our Chief Editors. Read the winning articles.