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Fractional heat conduction in a rectangular plate with bending moments

Warbhe Shrikant

Journal of Applied Mathematics and Computational Mechanics

2020

Vol. 19, nr 4

115--126

In this research work, we consider a thin, simply supported rectangular plate defined as 0 ≤ x ≤ a, 0 ≤ y ≤ b, 0 ≤ z ≤ c and determine the thermal stresses by using a thermal bending moment with the help of a time dependent fractional derivative. The constant temperature is prescribed on the surface y = 0 and other surfaces are maintained at zero temperature. A powerful technique of integral transform is used to find the analytical solution of initial-boundary value problem of a thin rectangular plate. The numerical result of temperature distribution, thermal deflection and thermal stress component are computed and represented graphically for a copper plate.

On Hermite-Hadamard type inequalities for s-convex mappings via fractional integrals of a function with respect to another function

Budak H., Sarikaya M. Z.

Fasciculi Mathematici

2016

Nr 57

25--36

In this paper, we obtain some Hermite-Hadamard type inequalities for s-convex function via fractional integrals with respect to another function which generalize the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. The results presented here provide extensions of those given in earlier works.

An approximation of the fractional integrals using quadratic interpolation

Błaszczyk T., Siedlecki J.

Journal of Applied Mathematics and Computational Mechanics

2014

Vol. 13, nr 4

13--18

In this paper we present a numerical scheme to calculations of the left fractional integral. To calculate it we use the fractional Simpson’s rule (FSR). The FSR is derived by applying quadratic interpolation. We calculate errors generated by the method for particular functions and compare the obtained results with the fractional trapezoidal rule (FTR).