Research Article Soliton Solutions of Generalized Third Order Time-Fractional KdV Models Using Extended He-Laplace Algorithm Mubashir Qayyum , 1 Efaza Ahmad, 1 Sidra Afzal , 1 and Saraswati Acharya 2 1 Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore, Pakistan 2 Kathmandu University School of Science, Dhulikhel, Nepal CorrespondenceshouldbeaddressedtoSaraswatiAcharya;saraswati.acharya@ku.edu.np Received 29 August 2022; Accepted 8 October 2022; Published 25 October 2022 AcademicEditor:AbdellatifBenMakhlouf Copyright©2022MubashirQayyumetal.isisanopenaccessarticledistributedundertheCreativeCommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this research, the He-Laplace algorithm is extended to generalized third order, time-fractional, Korteweg-de Vries (KdV) models. In this algorithm, the Laplace transform is hybrid with homotopy perturbation and extended to highly nonlinear fractionalKdVs,includingpotentialandBurgersKdVmodels.Time-fractionalderivativesaretakeninCaputosensethroughout the manuscript. Convergence and error estimation are confirmed theoretically as well as numerically for the current model. Numerical convergence and error analysis is also performed by computing residual errors in the entire fractional domain. Graphicalillustrationsshowtheeffectoffractionalparameteronthesolutionas2Dand3Dplots.AnalysisrevealsthattheHe- Laplace algorithm is an efficient approach for time-fractional models and can be used for other families of equations. 1. Introduction Inthelastfewdecades,fractionalcalculushasoutperformed ordinary calculus because basic calculus has reached to its peak.Engineersandscientistsarefocusingonthefractional models and their solutions due to their ability to provide more meaningful insight of physical phenomena with memoryeffectssuchasfractionalCassonfluidwithramped walltemperature[1],fractionalSEIRmodelofCovid19[2], fractional dual-phase-lag thermoelastic model [3], novel fractionaltime-delayedgreyBernoulliforecastingmodel[4], fractal fractional model of drilling nono-liquids [5] and stability of fractional quasi-linear impulsive integro-differ- entialsystems[6].ispermitsamoreaccuratedescription of real-world situations than the basic integral order. Well- known scientists including Joseph [7], Miller and Ross [8], Caputo [9], and Riemann [10] have made a significant contribution towards the foundation of fractional calculus. Fractional calculus provides a more accurate and realistic depiction of various phenomena in quantum physics [11], oceanography [12], fluid mechanics [13], and engineering [14]. In addition, fractional calculus is used to simulate the damping behavior of different materials and substrates, fi- nancial models, and many other scenarios. Solitary wave equations like (1+1)-dimensional Mikhailov–Novikov–Wang equation (15), RLW equation (16), complex Ginzburg–Landau model [17], and Korteweg anddeVriesequations[18]haveassembledalotofinterest from researchers. Among them, the most relevant family is KdV equations which also provide a foundation for other models. During 1895, Korteweg and de Vries first modeled the classical KdV equation [18]. ese equations are highly nonlinear and describe wave structures in crystal lattice, plasma, water, and density stratified ocean waves, etc., that are explored by many researchers. Heydari et al. observed fractional KdV-burger’s equation by discrete Chebyshev polynomials[19],secondorderdifferenceschemesfortime- fractional KdV-burger’s is solved by Cen et al. [20], frac- tionalKaup–KupershmidtequationisanalyzedbyShahetal. [21],Iqbaletal.[22]appliedAtangana-Baleanuderivativeon fractional Kersten–Krasil’shchik coupled KdV-mKdV sys- tem. KdV equations are also used in string theory with continuum limit. Similarly, the study of many physical as- pects through KdV equations in quantum field theory, Hindawi Complexity Volume 2022, Article ID 2174806, 14 pages https://doi.org/10.1155/2022/2174806