Combined Effects in Singular Elliptic Problems in Punctured Domain by Imed Bachar, Habib Mâagli, Hassan Eltayeb

“…The paper deals with nonlinear elliptic differential equations subject to some boundary value conditions in a regular bounded punctured domain. …”
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Modular multilevel converter periodic trajectory determination — A generic Fourier-based collocation method by Philippe De Rua, Jef Beerten

“…In the case of the MMC, the periodic trajectory determination is challenging due to nonlinearity and delays in the differential equations, in particular when control dynamics are taken into account. …”
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Mathematical model and stability of SWCNT- and MWCNT-based nanofluid flow with thermal and chemically reactive effects inside a porous vertical cone by Haihua Xu, Fuad A. Awwad, Emad A. A. Ismail, Waris Khan

“…Based on the flow assumptions, the fundamental flow equations are modeled as partial differential equations (PDEs). Using the appropriate transformation, the PDEs are converted to ordinary differential equations and then solved via RK4 in MATLAB. …”
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Design of Morlet Wavelet Neural Networks for Solving the Nonlinear Van der Pol–Mathieu–Duffing Oscillator Model by Ali Hasan Ali, Muhammad Amir, Jamshaid Ul Rahman, Ali Raza, Ghassan Ezzulddin Arif

“…We develop an MWNN-based fitness function to predict the dynamic behavior of nonlinear Vd-PM-DO differential equations. Then, we apply a novel hybrid approach combining WCA and ABC to optimize this fitness function, and determine the optimal weight and biases for MWNN. …”
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Parameter estimation in a structured erythropoiesis model by Azmy S. Ackleh, Jeremy J. Thibodeaux

“…We develop a numerical method for estimating parameters in astructured erythropoiesis model consisting of a nonlinear system ofpartial differential equations. Convergence theory for the computedparameters is provided. …”
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Positive Solutions of a Generalized Nonautonomous Fractional Differential System by Mohammed S. Abdo, Heba Y. Zahran, El Sayed Yousef, Emad E. Mahmoud, Abdel-Haleem Abdel-Aty

“…In this work, we investigate the existence and uniqueness of positive solutions to a system of nonautonomous fractional differential equations. The fractional derivative of the system at hand is ψ- Riemann–Liouville fractional derivative. …”
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New Modification on Heun’s Method Based on Contraharmonic Mean for Solving Initial Value Problems with High Efficiency by Abushet Hayalu Workie

“…In this paper, small modification on Improved Euler’s method (Heun’s method) is proposed to improve the efficiency so as to solve ordinary differential equations with initial condition by assuming the tangent slope as an average of the arithmetic mean and contra-harmonic mean. …”
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Calculation of bending deflection and stresses of a pipe with flowing fluid in the case of variable ground load by Rimantas Didžgalvis, Antanas Sudintas, Irena Tiknevičienė

“…Using the methods of approximate solutions of differential equations, the analytical pipe bend dynamic expressions were given at the case, when the ground load minimises expo­nentially. …”
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Application of Conformable Sumudu Decomposition Method for Solving Conformable Fractional Coupled Burger’s Equation by Hassan Eltayeb, Said Mesloub

“…It is an approximate analytical method, which can be used to solve linear and nonlinear partial differential equations. In this work, one-dimensional conformable functional Burger’s equation has been solved by applying conformable double Sumudu decomposition. …”
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A New Fractional Representation of the Higher Order Taylor Scheme by Iqbal M. Batiha, Iqbal H. Jebril, Amira Abdelnebi, Zoubir Dahmani, Shawkat Alkhazaleh, Nidal Anakira

“…In this work, we suggest a new numerical scheme called the fractional higher order Taylor method (FHOTM) to solve fractional differential equations (FDEs). Using the generalized Taylor’s theorem is the fundamental concept of this approach. …”
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Fast Attitude Maneuver of a Flexible Spacecraft with Passive Vibration Control Using Shunted Piezoelectric Transducers by Bassam A. Albassam

“…To simplify the analysis, the nonlinear ordinary differential equations of motion are then obtained using the assumed mode method. …”
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Existence and Stability of Square-Mean S-Asymptotically Periodic Solutions to a Fractional Stochastic Diffusion Equation with Fractional Brownian Motion by Jia Mu, Jiecuo Nan, Yong Zhou

“…In this paper, a generalized Gronwall inequality is demonstrated, playing an important role in the study of fractional differential equations. In addition, with the fixed-point theorem and the properties of Mittag–Leffler functions, some results of the existence as well as asymptotic stability of square-mean S-asymptotically periodic solutions to a fractional stochastic diffusion equation with fractional Brownian motion are obtained. …”
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Analytic Approximation of the Solutions of Stochastic Differential Delay Equations with Poisson Jump and Markovian Switching by Hua Yang, Feng Jiang

“…Most SDDEsPJMSs cannot be solved explicitly as stochastic differential equations. Therefore, numerical solutions have become an important issue in the study of SDDEsPJMSs. …”
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Degenerate Differential Operators with Parameters by Veli B. Shakhmurov

“…In applications, the nonlocal boundary value problems for degenerate elliptic partial differential equations and for systems of elliptic equations with parameters on cylindrical domain are studied.…”
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Application of the Multistep Generalized Differential Transform Method to Solve a Time-Fractional Enzyme Kinetics by Ahmed Alawneh

“…This enzyme-substrate reaction is formed by a system of nonlinear ordinary differential equations of fractional order. The fractional derivatives are described in the Caputo sense. …”
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Integral invariant manifold method applied to a mathematical model of osteosarcoma by Ophir Nave

“…These interactions are described by nonlinear ordinary differential equations. By applying the MIM method, two critical dynamic variables (Cancer cells and Necrotic cells) were identified, providing insights into the dynamics of osteosarcoma over time during treatment.…”
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Gluing for the Einstein constraint equations by Corvino, Justin

“…Initial data for the Einstein equations must satisfy a system of nonlinear partial differential equations, the Einstein constraint equations. …”
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Dynamic Properties of the Solow Model with Increasing or Decreasing Population and Time-to-Build Technology by Luca Guerrini, Mauro Sodini

“…The analytical results are obtained using the recent technique introduced by Beretta and Kuang (2002) in the studying of delayed differential equations with delay-dependent coefficients in characteristic equation. …”
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The Improved Generalized tanh-coth Method Applied to Sixth-Order Solitary Wave Equation by M. Torvattanabun, J. Simmapim, D. Saennuad, T. Somaumchan

“…This method is a powerful and advantageous mathematical tool for establishing abundant new traveling wave solutions of nonlinear partial differential equations. The new exact solutions consisted of trigonometric functions solutions, hyperbolic functions solutions, exponential functions solutions, and rational functions solutions. …”
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The Existence of Solution for a k-Dimensional System of Multiterm Fractional Integrodifferential Equations with Antiperiodic Boundary Value Problems by Dumitru Baleanu, Sayyedeh Zahra Nazemi, Shahram Rezapour

“…There are many published papers about fractional integrodifferential equations and system of fractional differential equations. The goal of this paper is to show that we can investigate more complicated ones by using an appropriate basic theory. …”
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