Preface to a thematic special issue of methods of mathematics and fractional calculus

Abstract

Preface to a thematic special issue of methods of mathematics and fractional calculus Mathematics is a common and widespread language that is not spoken very well in different parts of the world. This language also occurs in diverse forms that are required in different methods and applications. Today, mathematics is used everywhere from sciences and engineering to foreign languages research and the frontiers of social sciences. The key objective of this thematic special issue has been to offer typical attention on the latest advances and trends in different methods of mathematics and fractional calculus. Given the increasingly wide branches of mathematics, it is impossible to encapsulate a thorough representation of the selected topics in a single journal issue. However, it is possible to proffer a thematic special issue to bring together diverse fields of mathematics as well as a range of researchers from different parts of the world to represent a valued panel that addresses the different aspects and methods of mathematics, from pure, applied mathematics to fractional calculus.Manuscripts in this thematic special issue were requested through a general call and by invitation. It also includes selected papers that were presented at the International Conference on Fractional Differentiation and its Applications-ICFDA'18 held in Amman, Jordan, on July 16-18, 2018. All submissions were subject to a rigorous peer-review process following the well-known policies and standards of the Mathematical Methods in the Applied Sciences journal. Every submission was reviewed by at least two internationally established experts in the topic of that paper. The total number of papers received in response to the call of this thematic special issue was 90. Forty-nine papers were rejected after the peer-review process, and 41 were accepted upon up to three revisions and after an agreement was reached by the referees and the editors. Therefore, the rejection rate for this issue is 54.45%, which is one of the indicators of the high standards and quality considered when preparing this thematic special issue.In the following, we give a sense of the 41 accepted papers and the diversity of this thematic special issue where all papers are listed in references by their authors, title and DOI. The first paper by Dassios and Baleanu 1 investigates a class of singular linear systems of fractional differential equations with given inconsistent initial conditions. Validation of the proposed theory and analysis were carried out through numerical examples. Boumenir and Tuan 2 show that it is possible to uniquely recover the coefficient of an one-dimensional fractional diffusion equation from a single boundary measurement. An algorithm based on the well-known Gelfand-Levitan inverse spectral theory of Sturm-Liouville operators was developed and validated. The paper by Senol et al 3 deals with numerical methods for a KdV-like model. It was shown that the developed methods for the model equations are user-friendly and can be easily implemented to other...