We propose a high order explicit finite difference method for fractional advection diffusion equations. These equations can be obtained from the standard advection diffusion equations by replacing the second order spatial derivative by a fractional operator of order α with 1 < α ≤ 2. This operator is defined by a combination of the left and right Riemann–Liouville fractional derivatives. We stu...

A model of fractional-order of thermoelasticity is applied to study a 2D problem of mode-I crack in a fibre-reinforced thermal environment. The crack is under prescribed distributions of heat and pressure. The normal mode analysis is applied to deduce exact formulae for displacements, stresses, and temperature. Variations of field quantities with the axial direction are illustrated graphically....

in this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-laplacian fractional order differential equations. we use schauder&apos;s fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. we include some examples to show the applicability of our results.

in this paper, we prove the existence of the solution for boundary value prob-lem(bvp) of fractional dierential equations of order q 2 (2; 3]. the kras-noselskii&apos;s xed point theorem is applied to establish the results. in addition,we give an detailed example to demonstrate the main result.