The work in this paper is four-fold. Firstly, we introduce an alternative approach to solve fractional ordinary differential equations as expected value of a random time process. Using the latter, present interesting numerical based on Monte Carlo integration simulate solutions and partial equations. Thirdly, show that allows us find fundamental for (PDEs), which derivative Caputo sense space o...

Abstract In the present research study, time-fractional hyperbolic telegraph equations are solved iteratively using natural transform in one, two, and three dimensions. The fractional derivative is considered Caputo sense. These serve as a model for wave theory process of signal processing transmission electric impulses. To evaluate validity effectiveness suggested strategy, graphical compariso...

We develop efficient numerical methods for fractional order PDEs, and employ them to investigate viscoelastic constitutive laws for arterial wall mechanics. Recent simulations using one-dimensional models [1] have indicated that fractional order models may offer a more powerful alternative for modeling the arterial wall response, exhibiting reduced sensitivity to parametric uncertainties compar...

In this paper, we present a comparison of several important methods to solve fuzzy partial differential equations (PDEs). These include the reduced transform method (RDTM), Adomian decomposition (ADM), Homotopy perturbation (HPM), and analysis (HAM). A distinguishing practical feature these techniques is administered without need use discretion or restricted assumptions. Moreover, investigate (...

In this study, we establish exact solutions of fractional Kawahara equation by using the idea of [Formula: see text]-expansion method. The results of different studies show that the method is very effective and can be used as an alternative for finding exact solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The solitary wave solutions are expressed by the hyperbolic, t...