We introduce the Hahn quantum variational calculus. Necessary and sufficient optimality
conditions for the basic, isoperimetric, and Hahn quantum Lagrange problems, are studied …

ω ω We introduce its fundamental set of solutions when the coefficients are constant and the
Wronskian associated with, q D ω. Hence, we obtain the corresponding Liouville's formula …

This chapter introduces a comprehensive study for Sturm–Liouville theory of the q, ω-Hahn
difference operators in the regular setting. We define a Hilbert space of q, ω-square …

Hahn introduced the difference operator D q, ω f (t)=(f (qt+ ω)− f (t))/(t (q− 1)+ ω) in 1949,
where 0< q< 1 and ω> 0 are fixed real numbers. This operator extends the classical …

In this paper, we consider a strictly increasing continuous function β, and we present a
general quantum difference operator D β D_β which is defined to be D β f (t)=(f (β (t))− f …

There are several attempts to unify continuous and discrete mathematics. One of the main
approaches is the time scale which is recently founded by Stefan Hilger in his Ph. D. thesis …

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In this paper, we study a nonlocal boundary value problem for a second-order Hahn
difference equation. Our problem contains two Hahn difference operators with different …

Many physical phenomena are described by equations involving nondifferentiable functions,
eg, generic trajectories of quantum mechanics (Feynman and Hibbs 1965). Several different …

The quantum calculus deals with quantum derivatives and integrals, and has proven to be
relevant for quantum mechanics. It allows to deal with continuous functions, which do not …