Preface: Special issue on fractional differential equations, fuzzy analysis, graph theory and applied mathematics

Mani Mallika Arjunan; Sundarapandian Vaidyanathan; Anbalagan Pratap

Mani Mallika Arjunan School of Arts, Science and Humanities, SASTRA Deemed to be University, Thanjavur-613401, Tamil Nadu, India.
Sundarapandian Vaidyanathan Centre for Control Systems, Vel Tech University, Vel Nagar, Avadi, Chennai-600062, Tamil Nadu, India
Anbalagan Pratap Research Centre for Wind Energy Systems, Kunsan National University, Gunsan-si-54150, South Korea

Abstract

This special issue ``Fractional Differential Equations, Fuzzy Analysis, Graph Theory and Applied Mathematics", dedicated to first National Conference on Recent Developments in Fractional Calculus and its Applications [https://www.sastra.edu/rdfca2022/], Department of Mathematics, School of Arts, Science and Humanities, SASTRA Deemed to be University, Thanjavur-613401, Tamil Nadu, India, November 18$^{th}$ \& 19$^{th}$, 2022, contains papers on various topics in pure and applied mathematics including, in particular, such areas as fractional differential equations, fuzzy analysis, graph theory and some applied problems.

The relationship between current applied scientific research and pure mathematics disciplines like functional analysis, fractional differential equations, and graph theory is well acknowledged. In order to explore a wide range of challenges in applied sciences, it is crucial to use the methods and results of these domains.

The development of progressively complicated mathematical tools is required due to the increasing complexity of mathematical models in applications. This encourages researchers to look for new connections and/or descriptions in mathematical models of the phenomena they are studying that can help them enhance their models.

On the one hand, significant improvements in functional analysis lead to improvements in the theory of fractional differential equations as mathematical models in applied sciences, and thus to the development of applications. On the other hand, these improvements in turn lead to the creation of new applications. Graphs may also be used to model a broad variety of interactions and processes relating to physical systems, biological systems, social systems, and information systems.
Graphs are a useful tool for representing a wide variety of practical situations. The term network is sometimes defined to mean a graph in which attributes (such as names) are associated with the vertices and edges. Network science is the field that expresses and understands real-world systems in the form of a network. Some of the papers are invited papers.