Fractional calculus formulas for Mathieu-type series and generalized Mittag-Leffler function

Abstract

Fractional calculus is allowing integrals and derivatives of any positive order (the term 'fractional' kept only for historical reasons), which can be considered a branch of mathematical physics which mainly deals with integro-differential equations, where integrals are of convolution form with weakly singular kernels of power-law type. In recent decades fractional calculus has won more and more interest in applications in several fields of applied sciences. In this line, our main object to investigate image formulas of generalized fractional hypergeometric operators involving the product of Mathieu-type series and generalized Mittag-Leffler function. We also consider some interesting special cases of derived results by specializing suitable value of the parameters.

Best approximations of the ϕ-Hadamard fractional Volterra integro-differential equation by matrix valued fuzzy control functions

“…Using the fixed point technique (Alternative theorem), we study HUR stability of the φ-Hadamard fractional Volterra integro-differential equation (23) in MVFB-space (W, S , ). Our results can apply to improve recent results [17] and by methods used in this paper we can extend some fractional Volterra integro-differential equations in MVFBspaces [18][19][20].…”

Radu–Miheţ Method for the Existence, Uniqueness, and Approximation of the ψ-Hilfer Fractional Equations by Matrix-Valued Fuzzy Controllers

“…Our results can be applied to improve recent results [5], and by the methods used in this paper, we can extend some fractional Volterra integro-differential equations in MVF-k-Bspaces [11][12][13][14].…”

Existence–Uniqueness and Wright Stability Results of the Riemann–Liouville Fractional Equations by Random Controllers in MB-Spaces

“…In 2008, Mihet and Radu [16,17] introduced a new method to investigate random stability in MB-spaces and then some authors used this method to get stability results for new equations [18][19][20][21][22][23][24][25][26][27][28][29][30]. Here, we use the Mihet and Radu method and Theorem 1 to investigate random Wright stability of (3) and improve recent results [31]; we can suggest [32][33][34] for more details.…”