Abstract
In this paper, we present the exact solutions of the Parabolic-like equations and Hyperbolic-like equations with variable coefficients, by using Homotopy perturbation transform method (HPTM). Finally, we extend the results to the time-fractional differential equations.
 Keywords: Caputo’s fractional derivative, fractional differential equations, homotopy perturbation transform method, hyperbolic-like equation, Laplace transform, parabolic-like equation.
Highlights
The Parabolic-like and Hyperbolic-like equations can be used to describe wide variety of phenomena such as sound, heat, diffusion, electrostatics, electrodynamics, fluid dynamics, elasticity, or quantum mechanics
We used the homotopy perturbation transform method (HPTM). These problems have been studied by some researchers by using (ADM) and (HPM) see for example [12]and [18]
In this paper, we have seen that the coupling of homotopy perturbation method (HPM) and the Laplace transform, proved very effective to solve certain type of partial and fractional partial differential equations
Summary
The Parabolic-like and Hyperbolic-like equations can be used to describe wide variety of phenomena such as sound, heat, diffusion, electrostatics, electrodynamics, fluid dynamics, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalized in terms of Parabolic-like equations and Hyperbolic-like equations. For solving these equations, we used the homotopy perturbation transform method (HPTM). We used the homotopy perturbation transform method (HPTM) These problems have been studied by some researchers by using (ADM) and (HPM) see for example [12]and [18].
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