New results involving Riemann zeta function using its distributional representation
Date
2022
Authors
Tassaddiq, Asifa
Srivastava, Rekha
Journal Title
Journal ISSN
Volume Title
Publisher
Fractal and Fractional
Abstract
The relation of special functions with fractional integral transforms has a great influence
on modern science and research. For example, an old special function, namely, the Mittag–Leffler
function, became the queen of fractional calculus because its image under the Laplace transform
is known to a large audience only in this century. By taking motivation from these facts, we use
distributional representation of the Riemann zeta function to compute its Laplace transform, which
has played a fundamental role in applying the operators of generalized fractional calculus to this
well-studied function. Hence, similar new images under various other popular fractional transforms
can be obtained as special cases. A new fractional kinetic equation involving the Riemann zeta
function is formulated and solved. Thereafter, a new relation involving the Laplace transform of
the Riemann zeta function and the Fox–Wright function is explored, which proved to significantly
simplify the results. Various new distributional properties are also derived.
Description
Keywords
delta function, Riemann zeta-function, fractional transforms, Fox-Wright function, generalized fractional kinetic equation
Citation
Tassaddiq, A. & Srivastava, R. (2022). “New results involving Riemann zeta function using its distributional representation.” Fractal and Fractional, 6(5), 254. https://doi.org/10.3390/fractalfract6050254