Dr. Sanket Tikare is an assistant professor in the Department of Mathematics, at Ramniranjan Jhunjhunwala College, which is an empowered autonomous college affiliated with the University of Mumbai, India. He completed Ph.D. in Mathematics, from Shivaji University, Kolhapur, India, in the year 2012. He specializes in applied analysis. His research areas of interest include differential equations, difference equations, dynamic equations on time scales, quantum calculus and equations.Svetlin G. Georgiev is a mathematician who works on various aspects of mathematics. Currently, he focuses on ordinary and partial differential equations, differential geometry, dynamic geometry on time scales, integral equations on time scales, theory of distributions and harmonic analysis.

• Elements of Generalized Quantum Calculus.- First-order β-Quantum Differential Inequalities.- Basic β-Inequalities.- β-Wirtinger-Type Inequalities.- β-Opial-Type Inequalities.- β-Lyapunov-Type Inequalities.