Fractional Functional Analysis and Applications

Dear Colleagues,

After the success of the Special Issue “Fractional Functional Analysis”—Journal of Function Spaces (2021), we are glad to open it again as an annual Special Issue in Mathematics and AppliedMath.

In the last decades, fractional calculus has grown in popularity and importance due mainly to several applications in the widespread fields of mathematics, physics, engineering, etc. In particular, fractional calculus is now widely applied in electromagnetism, dynamical systems, PDEs, etc.

Fractional calculus represents one of the most interesting research fields in contemporary mathematics. Several fractional operators have found many real-world applications due to their properties of interpolation between operators of integer order. In addition, fractional function spaces have been widely applied for solving differential, integral, and integro-differential equations in both pure and applied mathematics. In the last twenty years, considerable attention has been paid to fractal operators. Several publications have shown interest in this regard, especially towards the link with wavelet analysis. Consequently, fractional functional analysis can be seen as a link between wavelet analysis, fractional geometry and, more generally, between different fields of applied functional analysis. In particular, fractional functional analysis extends the concept of function spaces to function spaces of fractional dimensions, opening new developments in both functional analysis and fractional calculus.

In this Special Issue, we invite and welcome reviews, expository, and original papers dealing with recent advances in fractional calculus; and, from a more general point of view, all theoretical and practical studies in pure and applied mathematics focused on this topic.

The main topics of this Special Issue include (but are not limited to):

• Fractional differential equations.
• Fractional function spaces.
• Commutators of fractional integral operators.
• Fractional calculus via Mittag-Leffler functions.
• Leibniz algebras, fractional calculus, and function spaces of symmetric functions.
• Fractional differential and integral equations.
• Fractional calculus, function space, and approximation theory.
• Fractional models in applied science.

This is a joint Special Issue with Mathematics.

You may choose our Joint Special Issue in Mathematics.

Dr. Emanuel Guariglia
Guest Editor

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