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Dynamical behavior for the approximate solutions and different wave profiles nonlinear fractional generalised pochhammer-chree equation in mathematical physics

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Abstract

In this paper, We have developed a variety of new approximate solutions for the nonlinear fractional generalized Pochhammer-Chree equation (FGPCEs) using the fractional homotopy perturbation transform method via the Caputo-Fabrizio fractional derivative(CFFD) of order \(\alpha \) where \(\alpha \in (1, 2].\) via Laplace transform technique.we investigate all concerned wave models that have been used in the examination for the propagation of harmonic waves in a cylindrical rod and several problems in fluid mechanics and wave theory in physics. Banach’s fixed point hypothesis is tested for governing the fractional-order model in order to establish the existence and uniqueness of the achieved solution. We considered the model in terms of arbitrary order with three cases and introduced corresponding numerical simulations to demonstrate and validate the effectiveness of the proposed algorithm. By assigning appropriate values to free parameters, dynamical wave structures of some approximate solutions are graphically demonstrated using 2D and 3D Fig. This method can also be used to approximate the solutions of other well-known equations in engineering physics, quantum field, and other applied sciences. Furthermore, various simulations are used to demonstrate the physical behaviors of the acquired solution with respect to fractional integer order.

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  1. Department of Mathematics, Patna Women’s College (Autonomous) Patna University, Bihar, 800001, India

    Ajay Kumar

  2. Department of Mathematics, Indira Priyadarshini Govt. girls post-graduate college of commerce, Haldwani, 263139, India

    Prachi Fartyal

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  1. Ajay Kumar
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Kumar, A., Fartyal, P. Dynamical behavior for the approximate solutions and different wave profiles nonlinear fractional generalised pochhammer-chree equation in mathematical physics. Opt Quant Electron 55, 1128 (2023). https://doi.org/10.1007/s11082-023-05416-1

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