This paper focuses on the usage of homotopy analysis method (HAM) to solve fractional heat conduction equation. In presented mathematical model, Caputo-type derivatives over time or space are considered. HAM, it is not necessary discretize considered domain, which its great advantage. As a result method, continuous function obtained, can be used for further analysis. For first time, equations, ...

The proposed study emphasis on to examine the temperature and stress distribution functionally graded thermosensitive rectangular plate. Caputo derivative of order 0 2 is applied analyses plate when subjected convection heat. Present article illustrated methodology mathematical model opt for framing expression address issues regarding properties ceramic based material affected by temperature. p...

In this article, we consider the stochastic heat equation du = (∆u + f(t, x))dt + P∞ k=1 g(t, x)δβ t , t ∈ [0, T ], with random coefficients f and g, driven by a sequence (βk)k of i.i.d. fractional Brownian motions of index H > 1/2. Using the Malliavin calculus techniques and a p-th moment maximal inequality for the infinite sum of Skorohod integrals with respect to (βk)k, we prove that the equ...