Pricing multi-asset financial derivatives with time-dependent parameters—Lie algebraic approach by C. F. Lo, C. H. Hui

“…Exploiting the dynamical symmetry of the pricing partial differential equations of the financial derivatives, the new method enables us to derive analytical closed-form pricing formulae very straightforwardly. …”
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A Family of Novel Exact Solutions to 2+1-Dimensional KdV Equation by Zhen Wang, Li Zou, Zhi Zong, Hongde Qin

“…We introduce two subequations with different independent variables for constructing exact solutions to nonlinear partial differential equations. In order to illustrate the efficiency and usefulness, we apply this method to 2+1-dimensional KdV equation, which was first derived by Boiti et al. (1986) using the idea of the weak Lax pair. …”
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Calculation of pipe bend and tension in case of fluid velocity pulsation by Rimantas Didžgalvis, Antanas Sudintas, Irena Tiknevičienė

“… The mathematical model of a bend pipe with a flowing fluid at a fluid pulsation was created. By solving differential equations, an analytical expression of solution is received, which may be well used for calculation of normal tension of the pipe at different ground load quantities and flow velocity pulsation. …”
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Dynamic Behaviors of an SEIR Epidemic Model in a Periodic Environment with Impulse Vaccination by Mei Yan, Zhongyi Xiang

“…By applying Floquet theory and the comparison theorem of impulsive differential equations, a threshold parameter which determines the extinction or persistence of the disease is presented. …”
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New Results for Multipoint Singular Boundary Value Problems on a Measure Chain by Yan Sun, Yongping Sun, Patricia J. Y. Wong

“…We study the existence and uniqueness of positive solutions for a class of singular m-point boundary value problems of second order differential equations on a measure chain. A sharper sufficient condition for the existence and uniqueness of Crd⁡1[0,T] positive solutions as well as Crd⁡1[0,T] positive solutions is obtained by the technique of lower and upper solutions and the maximal principle theorem.…”
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New Neumann System Associated with a 3 × 3 Matrix Spectral Problem by Fang Li, Liping Lu

“…As an application, solutions of the first nontrivial equation related to the 3 × 3 matrix spectral problem are decomposed into solving two compatible Hamiltonian systems of ordinary differential equations.…”
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A therapy inactivating the tumor angiogenic factors by Cristian Morales-Rodrigo

“…This paper is devoted to a nonlinear system of partial differential equations modeling the effect of an anti-angiogenic therapy based on an agent that binds to the tumor angiogenic factors. …”
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On Stability of Nonautonomous Perturbed Semilinear Fractional Differential Systems of Order α∈(1,2) by Mohammed M. Matar, Esmail S. Abu Skhail

“…We study the Mittag-Leffler and class-K function stability of fractional differential equations with order α∈(1,2). We also investigate the comparison between two systems with Caputo and Riemann-Liouville derivatives. …”
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The Small Time Asymptotics of SPDEs with Reflection by Juan Yang, Jianliang Zhai, Qing Zhou

“…We study stochastic partial differential equations with singular drifts and with reflection, driven by space-time white noise with nonconstant diffusion coefficients under periodic boundary conditions. …”
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Quasilinearization for the Boundary Value Problem of Second-Order Singular Differential System by Peiguang Wang, Tiantian Kong

“…We study the boundary value problems of second-order singular differential equations. At first, we reduce the BVPs to initial value problems of first-order singular integrodifferential equations and then we employ the quasilinearization method in studying the IVPs and obtain two monotone iterative sequences, which converge uniformly and quadratically to the unique solution of the IVPs. …”
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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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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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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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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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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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