Journal of Mahani Mathematical Research
Volume:9 Issue: 2, Summer and Autumn 2020

In this paper, we give some inequalities for dierentiable convex functions which are connected with the Hermite-Hadamard's integral inequality holding for convex functions. Also, we obtain some estimates to the right-hand side of Hermite-Hadamard inequality for functions whose absolute values of fourth derivatives raised to positive real powers are m-convex. Finally, some natural applications to special means of real numbers are given.

In this paper, we introduce a new subfamily of univalent functions defined in the open unit disk involving a fractional q-differintegral operator. Some results on coefficient estimates, weighted mean, convolution structure and convexity are discussed

In this paper, we establish Hermite-Hadamard inequalities for uniformly p-convex functions and uniformly q-convex functions. Also, we obtain some new inequalities of Hermite-Hadamard type for functions whose derivatives in absolute value are the class of uniformly p-convex.

In this paper we consider the one-dimensional variable-order time fractional diffusion equation where the order is $ q(x,t)in (0,1) $. One type of Caputo fractional derivative is introduced and to get a numerical technique, the time variable is discretized using a finite difference plan then we use a spectral collocation method to discretize the spatial derivative.‎ ‎In order to show the effectiveness and accuracy of this method‎, ‎some test problems are considered‎, ‎and it is shown that the obtained results are in very good agreement with exact solutions‎.