Research Projects

The q-calculus theory has gained interest from researchers due to its applications in various mathematical fields. Recent studies have introduced q-analogues of special matrices, such as Cesàro, Euler, Catalan, Fibonacci, and Pascal, and studied their domains in classical sequence spaces. The q-difference sequence spaces of second order have also been introduced, and the spectrum of q-difference operator of second order has been obtained over null and absolutely summable sequences. The q-analogues of difference sequence spaces of m^th order have also been introduced. The researchers aim to further advance these studies by developing q-difference operators of fractional order α and constructing sequence spaces via q-difference operator ∇_q^α in classical sequence spaces. They also aim to develop Cesàro or Euler q-difference sequence spaces of fractional order and explore the spectrum of q-difference operator of fractional order over the space of null sequences. These studies aim to advance summability and sequence spaces while generalizing previous results.