New Trends on Generalized Fractional Calculus, 2nd Edition

Dear Colleagues,

Recently, the study of general fractional differential operators has attracted the interest of the fractional calculus research community. In the literature, we can find several proposals for new definitions that categorise fractional calculus into general classes to unify different integro-differential operators. Examples of such classes are the ψ-fractional calculus with respect to a given function ψ, the weighted ψ-fractional calculus, and fractional calculus with general analytic kernels and Sonine kernels. This variety of classes is justified by the need for operators with different structures to successfully model a large number of processes and phenomena that exist in the real world.

For the study of fractional differential equations involving these general fractional derivatives, there is a need to develop new mathematical tools in the areas of integral transforms, special functions and their properties, generalised functions, and numerical methods, to mention a few. This Special Issue intends to contribute to the development and expansion of these topics within the scope of generalised fractional calculus.

We invite researchers to submit their original work, as well as review articles that discuss recent developments, applications, and connections with other fields of science.

Topics include (but are not limited to) the following:

• Mathematical theory of generalised fractional calculus.
• Integral transform methods.
• Special functions and their properties.
• Inequalities, maximum principles, and stability results.
• Initial and boundary value problems.
• Numerical analysis and algorithms.
• Fixed-point theory and applications in fractional calculus.
• Fractional differential equations arising in physical models. In particular, anomalous diffusion processes involving generalised fractional derivatives.
• Fractional stochastic differential equations.
• Fractional networks.

Dr. Milton Ferreira
Dr. Maria Manuela Fernandes Rodrigues
Dr. Nelson Felipe Loureiro Vieira
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.

• generalised fractional calculus
• fractional calculus with general analytic kernels
• ψ-fractional derivatives
• weighted fractional derivatives
• integral transforms
• special functions
• fractional inequalities
• fractional ODE and PDE
• initial and Boundary value problems

• New Trends on Generalized Fractional Calculus in Fractal and Fractional (9 articles)