Some estimates for Mittag-Leffler function in quantum calculus and applications

2023/02/01 by Michael Ruzhansky, Ruzhansky, Michael, Serikbol Shaimardan +3
Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2302.00532

openalex publication_date 2023/02/01 · openalex created_date 2023/02/04 · openalex updated_date 2026/07/28

Abstract

The study of the Mittag-Leffler function and its various generalizations has become a very popular topic in mathematics and its applications. In the present paper we prove the following estimate for the q-Mittag-Leffler function: (1)/(1+Γ_q(1-α)z)≤ e_α,1(-z;q)≤\frac11+Γ_q(α+1)^-1z. for all 0 < α< 1 and z>0. Moreover, we apply it to investigate the solvability results for direct and inverse problems for time-fractional pseudo-parabolic equations in quantum calculus for a large class of positive operators with discrete spectrum.

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