Some Nonlinear Fractional PDEs Involving β-Derivative by Using Rational exp−Ωη-Expansion Method by Haifa Bin Jebreen

“…Some fractional PDEs will convert to consider ordinary differential equations (ODEs) with the help of transformation β-derivative. …”
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Flow over Exponentially Stretching Sheet through Porous Medium with Heat Source/Sink by I. Swain, S. R. Mishra, H. B. Pattanayak

“…The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations and then solved numerically using a fourth-order Runge-Kutta method with a shooting technique. …”
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Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems by Mohamed Hannabou, Khalid Hilal, Ahmed Kajouni

“…In this paper, a class of nonlocal impulsive differential equation with conformable fractional derivative is studied. …”
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Lie Group Analysis of Unsteady Flow and Heat Transfer over a Porous Surface for a Viscous Fluid by M. B. Akgül, G. Sarı, M. Pakdemirli

“…Adopting the obtained symmetry groups, governing partial differential equations are converted into ordinary differential equations and then solved numerically. …”
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Unsteady MHD Mixed Convection Flow of Chemically Reacting Micropolar Fluid between Porous Parallel Plates with Soret and Dufour Effects by Odelu Ojjela, N. Naresh Kumar

“…A suitable similarity transformation is used to reduce the governing partial differential equations into nonlinear ordinary differential equations and then solved numerically by the quasilinearization method. …”
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Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis by N. Mindu, D. P. Mason

“…The migration of melt through the mantle of the Earth is governed by a third-order nonlinear partial differential equation for the voidage or volume fraction of melt. …”
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Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps by Tingting Ma, Xinzhu Meng, Zhengbo Chang

“…Using the comparison theorem of stochastic differential equations and asymptotic approaches, sufficient conditions for persistence in mean and extinction of three species are derived. …”
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Lie Symmetry Analysis for the General Classes of Generalized Modified Kuramoto-Sivashinsky Equation by Rong Qi, Muhammad Mobeen Munir, Nazish Younas, Muhammad Idrees, Jia-Bao Liu

“…Lie symmetry analysis of differential equations proves to be a powerful tool to solve or at least reduce the order and nonlinearity of the equation. …”
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An Approximate Solution for a Class of Ill-Posed Nonhomogeneous Cauchy Problems by Nihed Teniou, Salah Djezzar

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Chemical reaction and Soret impacts on MHD heat and mass transfer Casson hybrid nanofluid (MoS2+ZnO) flow based on engine oil across a stretching sheet with radiation by M. Radhika, Y. Dharmendar Reddy

“…The relevant similarity variables convert the governing nonlinear partial differential equations to ordinary differential equations (ODEs). …”
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Vieta-Lucas Collocation Technique for Examination of the Flow of Casson Fluid over a Slippery Stretching Sheet Which Is Impacted by Thermal Slip, Ohmic Dissipation, and Variable Th... by A. Eid, M. M. Khader, Ahmed M. Megahed

“…A collection of physical conditions on the sheet’s enclosing wall and the momentum and heat transport processes are expressed as partial differential equations (PDEs). Some of the similarity transformations are used to convert the collection of PDE into a system of ordinary differential equations. …”
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Finite Element Method Solution of Boundary Layer Flow of Powell-Eyring Nanofluid over a Nonlinear Stretching Surface by Wubshet Ibrahim, Gosa Gadisa

“…The simultaneous nonlinear partial differential equations governing the boundary layer flow are transformed to the corresponding nonlinear ordinary differential equations using similarity solution and then solved using Galerkin finite element method (GFEM). …”
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Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps by Guodong Liu, Xiaohong Wang, Xinzhu Meng, Shujing Gao

“…Furthermore, persistence in mean of the system is also investigated by using the theory of impulsive stochastic differential equations (ISDE) and delay differential equations (DDE). …”
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Chemical Reaction and Radiation Effects on MHD Flow of Oldroyd-B Fluid through Porous Medium Past an Exponentially Stretching Sheet with Heat Sink by Faisal Salah, Abdelmgid O. M. Sidahmed

“…The governing system of nonlinear partial differential equations has transformed into a system of ordinary differential equations using similarity transformations. …”
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Invariant Inhomogeneous Bianchi Type-I Cosmological Models with Electromagnetic Fields Using Lie Group Analysis in Lyra Geometry by Ahmad T. Ali

“…For this, Lie group analysis method is used to identify the generators that leave the given system of nonlinear partial differential equations (NLPDEs) (Einstein field equations) invariant. …”
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Heat Transfer Analysis on the Hiemenz Flow of a Non-Newtonian Fluid: A Homotopy Method Solution by Yasir Khan, Zdeněk Šmarda

“…The governing equations are transformed into dimensionless nonlinear ordinary differential equations by similarity transformation. Analytical technique, namely, the homotopy perturbation method (HPM) with general form of linear operator is used to solve dimensionless nonlinear ordinary differential equations. …”
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Thermal Diffusion and Diffusion Thermo Effects on the Viscous Fluid Flow with Heat and Mass Transfer through Porous Medium over a Shrinking Sheet by Nabil Eldabe, Mahmoud Abu Zeid

“…This phenomenon is modulated mathematically by a set of partial differential equations which govern the continuity, momentum, heat, and mass. …”
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Cotton-Type and Joint Invariants for Linear Elliptic Systems by A. Aslam, F. M. Mahomed

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New 4(3) Pairs Diagonally Implicit Runge-Kutta-Nyström Method for Periodic IVPs by Norazak Senu, Mohamed Suleiman, Fudziah Ismail, Norihan Md Arifin

“…These new methods are more efficient when compared with current methods of similar type and with the L-stable Runge-Kutta pair derived by Butcher and Chen (2000) for the numerical integration of second-order differential equations with periodic solutions.…”
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Similarity Solution of Marangoni Convection Boundary Layer Flow over a Flat Surface in a Nanofluid by Norihan Md. Arifin, Roslinda Nazar, Ioan Pop

“…The general governing partial differential equations are transformed into a set of two nonlinear ordinary differential equations using unique similarity transformation. …”
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