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This study first establishes several maximum and minimum principles involving the nonlocal Monge-Ampère operator and the multi-term time-space fractional Caputo-Fabrizio derivative. Based on the maximum principle established above, on the one hand, we show that a family of multi-term time-space fractional parabolic Monge-Ampère equations has at most one solution; on the other hand, we establish some comparison principles of linear and nonlinear multi-term time-space fractional parabolic Monge-Ampère equations.

In the present work, we construct a Dunkl generalization of the modified Szász-Mirakjan operators of integral form defined by Pǎltanea [1]. We study the approximation properties of these operators including weighted Korovkin theorem, the rate of convergence in terms of the modulus of continuity, second order modulus of continuity via Steklov-mean, the degree of approximation for Lipschitz class of functions and the weighted space. Furthermore, we obtain the rate of convergence of the considered operators with the aid of the unified Ditzian-Totik modulus of smoothness and for functions having derivatives of bounded variation.

In the paper the authors introduce the Kantorovich variant of Stancu operators based on Pólya-Eggenberger distribution. By making use of this new operator, we obtain some indispensable auxiliary results. We also deal with a Voronovskaja type asymptotic formula and some estimates of the rate of approximation involving modulus of smoothness, such as Ditzian-Totik modulus of smoothness. The rate of convergence for differential functions whose derivatives are bounded is also obtained.

In this article, for the incomplete H-functions, we obtain a set of new generating functions. The bilateral along with linear generating relations are derived for the incomplete H-functions. Many of the generating functions readily accessible in the literature are often deemed as implementations of the main findings. All the derived findings are of a natural type and can produce a variety of new results in generating function theory. [ABSTRACT FROM AUTHOR]

In this paper, we define a new extension of Srivastava's triple hypergeometric functions by using a new extension of Pochhammer's symbol that was recently proposed by Srivastava, Rahman and Nisar [H. M. Srivastava, G. Rahman and K. S. Nisar, Some extensions of the Pochhammer symbol and the associated hypergeometric functions, Iran. J. Sci. Technol. Trans. A Sci. 43 2019, 5, 2601–2606]. We present their certain basic properties such as integral representations, derivative formulas, and recurrence relations. Also, certain new special cases have been identified and some known results are recovered from main results. [ABSTRACT FROM AUTHOR]

In this paper, we derive certain Chebyshev type integral inequalities connected with a fractional integral operator in terms of the generalized Mittag-Leffler multi-index function as a kernel. Our key findings are general in nature and, as a special case, can give rise to integral inequalities of the Chebyshev form involving fractional integral operators present in the literature. [ABSTRACT FROM AUTHOR]