• Dr. Kamlesh kumar saini
• Mr. Pramod Kumar

In this paper we give some background theory on the concept of fractional calculus, in particular the Riemann-Liouville operators. We then investigate the Taylor-Riemann series using Osler’s theorem and obtain certain double infinite series expansions of some elementary functions. In the process of this we give a proof of the convergence of an alternative form of Heaviside’s series. A Semi-Taylor series is introduced as the special case of the Taylor-Riemann series when, and some of its relations to special functions are obtained via certain generating functions arising in complex fractional calculus.

Riemann-Liouville operators, Taylor-Riemann series, Heaviside’s series, Semi-Taylor series

"Riemann-Liouville Fractional Derivatives and the Taylor-Riemann Series", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.11, Issue 5, page no.f557-f564, May-2024, Available :http://www.jetir.org/papers/JETIR2405565.pdf

"Riemann-Liouville Fractional Derivatives and the Taylor-Riemann Series", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.11, Issue 5, page no. ppf557-f564, May-2024, Available at : http://www.jetir.org/papers/JETIR2405565.pdf