We introduce a sampling based machine learning approach, Monte Carlo physics informed neural networks (MC-PINNs), for solving forward and inverse fractional partial differential equations (FPDEs). As generalization of (PINNs), our method relies on deep network surrogates in addition to stochastic approximation strategy computing the derivatives DNN outputs. A key ingredient MC-PINNs is construc...

one of the ecient and powerful schemes to solve linear and nonlinear equationsis homotopy analysis method (ham). in this work, we obtain the approximate solution ofa system of partial dierential equations (pdes) by means of ham. for this purpose, wedevelop the concept of ham for a system of pdes as a matrix form. then, we prove theconvergence theorem and apply the proposed method to nd the a...

This paper considers a new Double Integral transform called Sumudu-Elzaki DSET. The combining of the DSET with semi-analytical method, namely variational iteration method DSETVIM, to arrive numerical solution nonlinear PDEs Fractional Order derivatives. proposed dual property decreases number calculations required, so these two methods leads calculating solution's speed. suggested technique is ...

In this paper, we generalize the theory of invariant subspace method to ( m + 1 ) -dimensional non-linear time-fractional partial differential equations for first time. More specifically, applicability and efficacy have been systematically investigated through 3 generalized diffusion–convection-wave equation along with appropriate initial conditions. This systematic investigation provides an im...

In this paper, we generalize the theory of invariant subspace method to ( m + 1 ) -dimensional non-linear time-fractional partial differential equations for first time. More specifically, applicability and efficacy have been systematically investigated through 3 generalized diffusion–convection-wave equation along with appropriate initial conditions. This systematic investigation provides an im...