Time-fractional partial differential equations: a novel technique for analytical and numerical solutions
Lokesh Kumar Yadav, Garima Agarwal, D. L. Suthar, S. D. Purohit
Abstract
We use the q-homotopy analysis Shehu transform method in this article to obtain analytical and numerical solutions to time fractional partial differential equations. We also give analytical solutions to two problems, as well as a comparison study in terms of absolute error with homotopy perturbation transform method, homotopy analysis transform method, and residual power series method to verify the suggested technique’s effectiveness and correctness. The numerical and graphical solutions achieved by the proposed method show that it is computationally accurate and may be used to obtain and investigate solutions to time fractional partial differential equations.
Topics & Concepts
Homotopy analysis methodMathematicsHomotopy perturbation methodPartial differential equationCorrectnessPower seriesApplied mathematicsMathematical analysisHomotopyAlgorithmPure mathematicsFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsNonlinear Waves and Solitons