Convolution Equations: Theory, Numerical Methods and Applications

Dear Colleagues, 

Convolution equations and related Riemann and Hilbert boundary value problems comprise an active and growing field in mathematics. This field involves a large number of independent but closely related disciplines. Convolution equations also include singular integral equations, hypersingular integral equations, Wiener–Hopf equations, integral equations with fractional integrals and derivatives, and many others.

It is not easy to list all areas in physics, engineering, and natural sciences where convolution equations play a key role, but some include: aerodynamics, electrodynamics, elasticity theory, automatic control theory, astrophysics, wave theory, materials science, and others.

Although many subjects known as “Convolution equations” have been known for over a century, they are being actively developed today.

Besides the branches mentioned above, singular integral equations and the related Riemann and Hilbert boundary value problems on fractals have been been actively studied over the last few decades.

In this Special Issue, we will present the current state of these areas and trace the connections between them.

This Special Issue will include works devoted to analytical methods for solving hypersingular integral equations, as well as approximate methods for solving weakly singular convolutional integral equations (Volterra and Fredholm), singular integral equations, hypersingular and polyhypersingular integral equations (linear and nonlinear) defined on various manifolds, integral equations with fractional integrals, Wiener–Hopf equations, Ambartsumian–Chandrasekhar equations, and systems of equations, which play an important role in the theory of light scattering in turbid media.

Numerical methods for solving integral equations rely upon efficient numerical methods for integral evaluation. This Special Issue also presents works dedicated to approximate methods for calculating singular and hypersingular integrals.

Prof. Dr. Ilya Boykov
Dr. Alla Boykova
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 250 words) can be sent to the Editorial Office for assessment.

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-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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.