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Uniqueness of a nonlinear integro-differential equation with nonlocal boundary condition and variable coefficients

Authors: Chenkuan, Li; Advisor: -; Co-Author: - (2023)

This paper studies the uniqueness of solutions to a two-term nonlinear fractional integro-differential equation with nonlocal boundary condition and variable coefficients based on the Mittag-Leffler function, Babenko’s approach, and Banach’s contractive principle. An example is also provided to illustrate the applications of our theorem.

Differentiation of integral Mittag-Leffler and integral Wright functions with respect to parameters

Authors: Alexander, Apelblat; Juan Luis, González-Santander; Advisor: -; Co-Author: - (2023)

Derivatives with respect to the parameters of the integral Mittag-Leffler function and the integral Wright function, recently introduced by us, are calculated. These derivatives can be expressed in the form of infinite sums of quotients of the digamma and gamma functions. In some particular cases, these infinite sums are calculated in closed-form with the help of MATHEMATICA. However, parameter differentiation reduction formulas are explicitly derived in order to check some of the results given by MATHEMATICA, as well as to provide many other new results.