Partohaghighi, MohammadAkgul, AliAsad, JihadWannan, Rania2024-12-242024-12-2420222473-6988https://doi.org/10.3934/math.2022959https://hdl.handle.net/20.500.12604/8394Heydari-Hosseininia (HH) fractional derivative is a newly introduced concept of fractional calculus which conquers the restrictions of non-singular fractional derivatives in the Caputo-Fabrizio (CF) and Atangana-Baleanu senses. For instance, it is not easy to get the closed-form of the fractional derivative of functions using CF because of the construction of its kernel function. In this paper, we present a powerful numerical scheme based on energy boundary functions to get the approximate solutions of the time-fractional inverse Burger equation containing HH-derivative: (HH)D(tau)(alpha)h(z, tau) - h(z, tau)h(z)(z, tau) = h(zz)(z, tau) + H(z, tau), which (HH)D(alpha)(tau )is the HH-derivative with regard to alpha-order. This problem has never been investigated earlier so, this is our motivation to work on this important problem. Some numerical examples are presented to verify the efficiency of the presented technique. Graphs of the exact and numerical solutions along with the plot of absolute error are provided for each example. Tables are given to see and compare the results point by point for each example.eninfo:eu-repo/semantics/openAccessOptimizationfractional inverse Burger equationHeydari-Hosseininia derivativeArticle791740317417Q1WOS:000835164600001Q12-s2.0-8513526428010.3934/math.2022959