Trends, directions for further research, and some open problems of fractional calculus
Kai Diethelm, Virginia Kiryakova, Yuri Luchko, J. A. Tenreiro Machado, Vasily E. Tarasov
Abstract
Abstract The area of fractional calculus (FC) has been fast developing and is presently being applied in all scientific fields. Therefore, it is of key relevance to assess the present state of development and to foresee, if possible, the future evolution, or, at least, the challenges identified in the scope of advanced research works. This paper gives a vision about the directions for further research as well as some open problems of FC. A number of topics in mathematics, numerical algorithms and physics are analyzed, giving a systematic perspective for future research.
Topics & Concepts
Scope (computer science)Calculus (dental)Fractional calculusPerspective (graphical)Key (lock)Relevance (law)Computer scienceOpen researchMathematicsManagement scienceApplied mathematicsArtificial intelligenceMedicineEngineeringPolitical scienceProgramming languageDentistryLawComputer securityWorld Wide WebFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsNonlinear Differential Equations Analysis