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This paper concentrates on addressing fractional inequalities for exponential type convex functions. By means of exponential-type convexity, we firstly establish Hermite-Hadamard (HH) type inequalities for fractional integrals with exponential kernels. Secondly, based on the discovered fractional identity by separating [a; b] to n equal subintervals, and the fact that the twice derivative in absolute value is exponential type convex, we present multipoint-based HH inequalities, which cover the trapezoid- and Bullen-type inequalities for n = 1 and 2, correspondingly. During the period, some numerical examples with graphs are provided to show the validity of the deduced inequalities. [ABSTRACT FROM AUTHOR]

Simpson inequalities for first-order differentiable convex functions and various fractional integrals have been studied extensively. However, Simpson type inequalities for twice-differentiable functions are researched slightly. Therefore, in the present paper, we endeavor to study fractional inequalities of Simpson type for twice-differentiable convex functions. To achieve this goal, we establish a new twicedifferentiable Simpson's identity by using tempered fractional integral operators. Based upon it, we prove several fractional Simpson type inequalities whose second derivatives in absolute value are convex. Finally, we give some examples to illustrate the correctness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper established the idea of minimum evdominating matrix of semigraph and calculated its energy. The minimum ev-dominating energy EmeD(G) of a semigraph G is the sum of the absolute values of the eigenvalues of the minimum ev-dominating matrix. Here some results are also derived in connection with the energy of minimum evdominating matrix. Some lower bounds are also established. [ABSTRACT FROM AUTHOR]