# Mathematical Analysis Is the Theoretical Basis of a Number of Mathematical Disciplines

A special issue of *Axioms* (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: **closed (31 October 2022)** | Viewed by 29928

## Special Issue Editors

**Interests:**analytical theory of differential equations; nonlinear differential equations; differential equations with fractional derivatives; mathematical modeling; computational mathematics

Special Issues, Collections and Topics in MDPI journals

**Interests:**dynamical systems; fractional systems; functional analysis

Special Issues, Collections and Topics in MDPI journals

## Special Issue Information

Dear Colleagues.

This issue is devoted to sections of mathematical disciplines that apply the basics of mathematical analysis to prove results in such areas as differential equations and optimal control, mathematical physics, mathematical problems of artificial intelligence, and interdisciplinary applications of mathematical theory—in particular when obtaining conditions for the solvability of differential equations in the analytical theory of differential equations; when proving the existence and uniqueness theorems of solutions of nonlinear differential equations with movable singular points both in the area of analyticity and in the vicinity of movable singular points, as well as when constructing analytical approximate solutions of such equations; when proving the existence and uniqueness theorems of solutions for equations with fractional derivatives and proving convergence during numerical calculations; when developing methods for substantiating mathematical models based on differential equations of both ordinary and fractional derivatives in various fields of human activity; when developing a mathematical apparatus of artificial intelligence elements to expand the capabilities of classical numerical methods; and when applying mathematical theory in the study of building structures and calculations.

It should be noted that the Special Issue is open to further ideas beyond the aforementioned topics.

We hope that this initiative will be attractive to experts in the field of the theory of differential equations with both ordinary and fractional derivatives, as well as their theoretical and practical applications. We recommend that you submit your current research for inclusion in a Special Issue.

Researchers working in this interdisciplinary field can present their original research results, as well as explanatory and review articles.

Contributions may be submitted on an ongoing basis before the deadline. After the review process, the materials will be selected for publication based on their quality and relevance.

Prof. Dr. Viktor N. Orlov

Prof. Dr. Michal Feckan*Guest Editors*

**Manuscript Submission Information**

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## Keywords

- the theorem of existence and uniqueness of the solution of a nonlinear differential equation in the field of analyticity
- the theorem of existence and uniqueness of the solution of a nonlinear differential equation in the vicinity of a moving singular point
- the theorem of the existence of a solution to a differential equation with fractional derivatives
- analytical approximate solution of a nonlinear differential equation in the field of analyticity, a priori and a posteriori error estimates
- analytical approximate solution of a nonlinear differential equation in the vicinity of a moving singular point, a priori and a posteriori error estimates
- approximate analytical and numerical solutions of a differential equation with fractional derivatives
- verification of the fractional derivative indicator for the mathematical model of the process under study
- mathematical justification for an equation with a fractional derivative as a model of the process under study
- mathematical models of building structures
- stability analysis of fractional differential equations

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