Special Issue "Fractional Dynamic Inequalities with Numerical Techniques and Its Application to Arbitrary Time Scales"
Deadline for manuscript submissions: 31 January 2024 | Viewed by 1852
Interests: special functions; orthogonal polynomials; differential equations; operator theory; multivariate approximation theory; Lie algebra
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This Special Issue is devoted to recent developments in the theory of dynamic inequalities and fractional calculus on time scales, including numerical examples such as Hermite–Hadamard’s inequality, Gronwall–Bellman’s inequality, Hardy’s inequality, Steffensen’s inequality, Hölder’s inequality, Opial’s inequality, Ostrowski’s inequality, and Hilbert’s inequality.
Inequalities lie at the heart of mathematical analysis, which is a major and important branch of mathematics. Throughout history, many researchers have discovered a great number of inequalities that are useful in many fields of mathematics. Furthermore, dynamic inequalities that provide explicit bounds on unknown functions have proved to be useful in the study of qualitative properties of the solutions of dynamic, differential, integral, and integrodifferential equations.
Fractional calculus, the theory of integrals and derivatives of non-integer order, has an important role in mathematical analysis and applications.
In 1988, Stephan Hilger introduced in his Ph.D. thesis a new theory, the theory of time scales, which builds bridges between continuous and discrete mathematics. The main idea was to prove a result for a dynamic inequality where the domain of the unknown function is a so-called time scale T, which is defined as an arbitrary closed subset of the real numbers R, to avoid proving results twice, once in the continuous case which leads to an integral inequality and once again on a discrete case which leads to a discrete inequality. Currently, the application of dynamic inequalities and fractional calculus to time scales is a subject of strong interest. It is the purpose of this Special Issue to collate some of the recent developments on this subject.
Prof. Dr. Clemente Cesarano
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