Theoretical and numerical study of profit in agricultural sector model using wavelet method by Yeshwanth R., Kumbinarasaiah S.

“…The operational matrices are used to simplify fractional differential equations to an algebraic system of equations. …”
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Irreversibility and Sensitivity analysis of MHD squeezing various shaped nanofluid flow between parallel permeable disks by Abdul Awal, Md. Sarwar Alam

“…The system of partial differential equations governing the flow is converted to a coupled of non-dimension ordinary differential equations. …”
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Analysis of the Three-Dimensional Dynamic Problems by Using a New Numerical Method by Yao Rong, Yang Sun, LiQing Zhu, Xiao Xiao

“…In this paper, the scaled boundary element method (SBFEM) is used to analyze the displacement and pore pressure response of saturated soil due to consolidation under dynamic load. The partial differential equations of linear problems are transformed into ordinary differential equations and solved along the radial direction. …”
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Analytical study of steady state axisymmetric stagnation-point gold–blood Casson nanofluid through a rotating stretchable disk by Usman Ali, Hamid Khan, Waris Khan, Emad E. Mahmoud, Marouan Kouki, Jabr Aljedani, Hakim AL Garalleh

“…By using scaling variables, the complex system of partial differential equations is simplified into a set of coupled high degree nonlinear ordinary differential equations with convective boundary conditions. …”
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Computational analysis of bioconvective MHD hybrid nanofluid flow of non-Newtonian fluid over cone/plate: A study based on the Cattaneo-Christov heat and mass flux model by P. Francis, P. Sambath, S. Noeiaghdam, U. Fernandez-Gamiz, S. Dinarvand

“…A similarity transformation is used to simplify the complex partial differential equations into ordinary differential equations, which are then solved using the Keller Box finite difference method. …”
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Thermodynamics and solar radiative analysis in Jeffery-Hamel flow through non-parallel channel by novel improved residual power series method by Mohamed Bouzidi, Mohsin Ul Haq, Ikram Ullah, Saira Shukat, Hijaz Ahmad, Mohammad Mahtab Alam, Hamid Khan, Marouan Kouki

“…The governing system of partial differential equations can be transformed into ordinary differential equations (ODEs) using suitable transformations. …”
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Application of DTM to heat source/sink in squeezing flow of iron oxide polymer nanofluid between electromagnetic surfaces by Reshu Gupta, A.B. Albidah, NFM Noor, Ilyas Khan

“…The governing partial differential equations (PDEs) for flow, heat, and mass transfer are transformed into nonlinear ordinary differential equations (ODEs) through the appropriate similarity transformation. …”
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A comprehensive numerical study exploring the significance of thermally reactive bioconvection in Falkner-Skan flow of Williamson nanomaterials influenced by activation energy and... by M. Israr Ur Rehman, Haibo Chen, Aamir Hamid, Wu Qian, Refka Ghodhbani, Mohamed Hussien

“…Similarity transformations are used to convert the system of partial differential equations into a system of ordinary differential equations, which are then numerically solved using the Runge–Kutta–Fehlberg (RKF-45) method. …”
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Nonstationary Fronts in the Singularly Perturbed Power-Society Model by M. G. Dmitriev, A. A. Pavlov, A. P. Petrov

“…The theory of contrasting structures in singularly perturbed boundary problems for nonlinear parabolic partial differential equations is applied to the research of formation of steady state distributions of power within the nonlinear “power-society” model. …”
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Existence Results for an Implicit Coupled System Involving $\xi$-Caputo and $p$-Laplacian Operators by Walid Benhadda, Abderrazak Kassidi, Ali El Mfadel, Elomari M'hamed

“…This paper aims to establish the existence and uniqueness of a solution to a coupled system of $\xi$-Caputo fractional differential equations involving the $p$-Laplacian operator in an arbitrary Banach space. …”
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Symmetry and Solution of Neutron Transport Equations in Nonhomogeneous Media by Ivan Tsyfra, Tomasz Czyżycki

“…The method is also applicable to nonstationary and nonintegrable in quadratures differential equations.…”
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Existence of Positive Solutions for a Class of px,qx-Laplacian Elliptic Systems with Multiplication of Two Separate Functions by Youcef Bouizem, Salah Mahmoud Boulaaras, Ali Allahem

“…The paper deals with the study of the existence of weak positive solutions for a new class of the system of elliptic differential equations with respect to the symmetry conditions and the right hand side which has been defined as multiplication of two separate functions by using the sub-supersolutions method (1991 Mathematics Subject Classification: 35J60, 35B30, and 35B40).…”
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Global stability for the prion equation with general incidence by Pierre Gabriel

“…We consider the so-called prion equation with the general incidence term introduced in [14], and we investigate the stability of the steady states.The method is based on the reduction technique introduced in [11].The argument combines a recent spectral gap result for the growth-fragmentation equation in weighted $L^1$ spaces and the analysis of a nonlinear system of three ordinary differential equations.…”
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Solution of Moving Boundary Space-Time Fractional Burger’s Equation by E. A.-B. Abdel-Salam, E. A. Yousif, Y. A. S. Arko, E. A. E. Gumma

“…The fractional Riccati expansion method is used to solve fractional differential equations with variable coefficients. To illustrate the effectiveness of the method, the moving boundary space-time fractional Burger’s equation is studied. …”
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Some Properties of Solutions to Multiterm Fractional Boundary Value Problems with p-Laplacian Operator by KumSong Jong, HuiChol Choi, KyongJun Jang, SongGuk Jong, KyongSon Jon, Ok Ri

“…In this paper, we study some properties of positive solutions to a class of multipoint boundary value problems for nonlinear multiterm fractional differential equations with p-Laplacian operator. Using the Banach contraction mapping principle, the existence, the uniqueness, the positivity, and the continuous dependency on m-point boundary conditions of the solutions to the given problem are investigated. …”
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Sociodynamics applied to the evolution of urban and regional structures by Wolfgang Weidlich

“…From it the set of nonlinear coupled differential equations for the quasi-meanvalues of the macrovariables can be derived.…”
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The Method of Lines for Ternary Diffusion Problems by Henryk Leszczyński, Milena Matusik

“…These equations are transformed by a discretization in space variables into systems of ordinary differential equations. The proposed ODEs satisfy the mass conservation law. …”
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Space-time caustics by Arthur D. Gorman

“…The Lagrange manifold (WKB) formalism enables the determination of the asymptotic series solution of linear differential equations modelling wave propagation in spatially inhomogeneous media at caustic (turning) points. …”
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Asian Option Pricing with Monotonous Transaction Costs under Fractional Brownian Motion by Di Pan, Shengwu Zhou, Yan Zhang, Miao Han

“…The method of partial differential equations was used to solve this model and the analytical expressions of the Asian option value were obtained. …”
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Singular boundary value problem on infinite time scale

“…<p>This paper deals with a class of singular boundary value problems of differential equations on infinite time scale. An existence theorem of positive solutions is established by using the Schauder fixed point theorem and perturbation and operator approximation method, which resolves the singularity successfully and differs from those of some papers. …”
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