Thermal Radiation and Buoyancy Effects on Heat and Mass Transfer over a Semi-Infinite Stretching Surface with Suction and Blowing by S. Shateyi

“…Appropriate transformations were employed to transform the governing differential equations to nonsimilar form. The transformed equations were solved numerically by an efficient implicit, iterative finite-difference scheme. …”
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Mixed Convection over an Inclined Wavy Surface in a Nanofluid Saturated Non-Darcy Porous Medium with Radiation Effect by Darbhasayanam Srinivasacharya, Poshala Vijay Kumar

“…The governing equations are transformed into a set of ordinary differential equations using the appropriate similarity transformation and then solved using the successive linearization method. …”
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Novel Stability Criteria of Nonlinear Uncertain Systems with Time-Varying Delay by Yali Dong, Shengwei Mei, Xueli Wang

“…By constructing the proposed Lyapunov-Krasovskii functional approach, continuous state feedback controllers are put forward, and the criteria which guarantee the exponential stabilization of the nonlinear systems with uncertainties and time-varying delay are established in terms of solutions to the standard Riccati differential equations. Furthermore, based on the Lyapunov method and the linear matrix inequality approach, the sufficient conditions of exponential stability for a class of uncertain systems with time-varying delays and nonlinear perturbations are derived. …”
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Traveling Wave Solutions of Space-Time Fractional Generalized Fifth-Order KdV Equation by Dianchen Lu, Chen Yue, Muhammad Arshad

“…At the end, three types of exact traveling wave solutions are obtained which indicate that the method is very practical and suitable for solving nonlinear fractional partial differential equations.…”
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Computing the Electric and Magnetic Matrix Green’s Functions in a Rectangular Parallelepiped with a Perfect Conducting Boundary by V. G. Yakhno, Ş. Ersoy

“…This method is based on approximation (regularization) of the Dirac delta function and its derivatives, which appear in the differential equations for magnetic and electric Green’s functions, and the Fourier series expansion meta-approach for solving the elliptic boundary value problems. …”
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Mathematical Modelling of the Transmission of Malaria. by Atubangire, Felix

“…The model takes in the ordinally differential equations. The basic reproduction number Ro is obtained. …”
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A Mathematical Model for the Dynamics of Income Distribution in the Presence of Production by Maria Letizia Bertotti

“…The framework is expressed in the form of a system of nonlinear ordinary differential equations, as many as the income classes are, involving transition probabilities. …”
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A Generalized Approach of Triple Integral Transforms and Applications by Rania Saadeh

“…We apply the general triple transform to solve some applications of various types of partial differential equations. The strength of the new approach is that it covers almost all integral transforms of order one, two, and three, and hence no need to find new formulas of triple integral transforms or to study the basic properties.…”
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A Multiresolution PDE-Based Deformable Surface for Medical Imaging Applications

“…<p>We recently developed a multiresolution PDE-based deformable surface whose deformation behavior is governed by partial differential equations (PDEs) such as the weighted minimal surface flow. …”
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Numerical Solutions for the Eighth-Order Initial and Boundary Value Problems Using the Second Kind Chebyshev Wavelets by Xiaoyong Xu, Fengying Zhou

“…A collocation method based on the second kind Chebyshev wavelets is proposed for the numerical solution of eighth-order two-point boundary value problems (BVPs) and initial value problems (IVPs) in ordinary differential equations. The second kind Chebyshev wavelets operational matrix of integration is derived and used to transform the problem to a system of algebraic equations. …”
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Linear algebra and differential geometry on abstract Hilbert space by Alexey A. Kryukov

“…The formalism itself and its applications in linear algebra, differential equations, and differential geometry are carefully analyzed.…”
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Stochastic Predator-Prey System Subject to Lévy Jumps by Xinzhu Meng, Xiaohong Wang

“…In addition, we obtain the sufficient conditions for almost sure permanence in mean and stochastic permanence of the system by using the theory of impulsive stochastic differential equations. Finally, we discuss the biological implications of the main results and show that the large noise can make the system go extinct. …”
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Discontinuous nonlocal conservation laws and related discontinuous ODEs – Existence, Uniqueness, Stability and Regularity by Keimer, Alexander, Pflug, Lukas

“…This fixed-point problem itself necessitates the study of existence, uniqueness and stability of a class of discontinuous ordinary differential equations. On the ODE level, we compare the solution type defined here with the well-known Carathéodory and Filippov solutions.…”
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The Investigation of MHD Williamson Nanofluid over Stretching Cylinder with the Effect of Activation Energy by Wubshet Ibrahim, Mekonnen Negera

“…Dimensionless ordinary differential equations are obtained from the modeled PDEs by using appropriate transformations. …”
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An Improved Version of Residual Power Series Method for Space-Time Fractional Problems by Mine Aylin Bayrak, Ali Demir, Ebru Ozbilge

“…The parameter λ allows us to establish the best numerical solutions for space-time fractional differential equations (STFDE). Since each problem has different Dirichlet boundary conditions, the best choice of the parameter λ depends on the problem. …”
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Determination of Number of Infected Cells and Concentration of Viral Particles in Plasma during HIV-1 Infections Using Shehu Transformation by M. Higazy, Sudhanshu Aggarwal, Y. S. Hamed

“…The mathematical model of HIV-1 infections contains a system of two simultaneous ordinary linear differential equations with initial conditions. Results depict that Shehu transformation is very effective integral transformation for determining the number of infected cells and concentration of viral particles in plasma during HIV-1 infections.…”
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Forecasting New Product Diffusion Using Grey Time-Delayed Verhulst Model by Yuhong Wang, Shulin Yang, Wuyong Qian, Xiaozhong Li

“…Taking account of the time-delayed phenomenon in diffusion of new products, we propose the time-delayed Verhulst model and then establish a grey time-delayed Verhulst model using the method of grey differential equations. The related parameter packets of this novel model are obtained under the rule of ordinary least squares (OLS). …”
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$\phi $-FEM for the heat equation: optimal convergence on unfitted meshes in space by Duprez, Michel, Lleras, Vanessa, Lozinski, Alexei, Vuillemot, Killian

“…Thanks to a finite element method, we solve numerically parabolic partial differential equations on complex domains by avoiding the mesh generation, using a regular background mesh, not fitting the domain and its real boundary exactly. …”
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Application of Fuzzy Fractional Kinetic Equations to Modelling of the Acid Hydrolysis Reaction by Ferial Ghaemi, Robiah Yunus, Ali Ahmadian, Soheil Salahshour, Mohamed Suleiman, Shanti Faridah Saleh

“…The method is computationally interesting, and the numerical results demonstrate the effectiveness and validity of the method for solving fuzzy fractional differential equations.…”
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The General Traveling Wave Solutions of the Fisher Equation with Degree Three by Wenjun Yuan, Qiuhui Chen, Jianming Qi, Yezhou Li

“…Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics.…”
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