In this paper, we derive a Mittag-Leffler function for real index and establish solutions of special type of fractional order differential equations (FDEs). The same concept is extended to discrete case by replacing polynomials into factorial polynomials and differentiation into l-difference operator. Moreover, numerical examples of our results are stated to validate our findings. The acquired results here have the ability to generate a wide range of formulas in relation to newer results. [ABSTRACT FROM AUTHOR]
In this paper we extend the notion of Melham sum to the Pell and Pell-Lucas sequences. While the proofs of general statements rely on the binomial theorem, we prove some spacial cases by the known Pell identities. We also give extensions of obtained expressions to the other recursive sequences. [ABSTRACT FROM AUTHOR]
In this paper, we study q-extension of Mittag-Leffler operators. We establish moments of these operators and estimate convergence results with the help of classical modulus of continuity. Also, we give weighted approximation property and A-statistically convergence of the operators L(β)n,q. [ABSTRACT FROM AUTHOR]
Based on Andrews' recent work on parity in partitions, this paper will prove two partition identities proposed by Andrews (2010), simplify two generating functions into single sum expressions and extend two double series expansions of the first and second q-exponential functions. [ABSTRACT FROM AUTHOR]