The Chini integrability condition in second order Lovelock gravity by Mohammed O. E. Ismail, Sunil D. Maharaj, Byron P. Brassel

“…We then determine a systematic approach to integrate the condition of pressure isotropy by showing that the canonical form is a Chini differential equation. The Chini invariant, which allows the master differential equation to be separable, is identified. …”
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Recognition of High Difference Features in Urban Planning Images Based on Morphological Filtering by Peipei Liu

“…This paper mainly studies the image enhancement method based on partial differential equation. By analysing the combination of partial differential equation theory and enhancement, aiming at the shortcomings of low recognition accuracy, high error rate, and long time consuming in the current method of urban planning image feature recognition, a feature enhancement and simulation of urban planning image based on partial differential equation method is proposed; the preprocessing of urban planning image is realized by collecting the urban planning image. …”
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Similar Construction Method of Solution for Solving the Mathematical Model of Fractal Reservoir with Spherical Flow by Cui-Cui Sheng, Jin-Zhou Zhao, Yong-Ming Li, Shun-Chu Li, Hu Jia

“…On the basis of similar structure of solution for a second-order linear differential equation's boundary value problem, and our analysis of the relationship between this similar structure and its kernel function, the differential equation, and the boundary conditions, we propose a new simple solution—similar constructive method of solution (SCMS)—and sum up its detailed steps. …”
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Modified Wiener equations by Will Watkins

“…This paper is concerned with a class of functional differential equations whose argument transforms are involutions. …”
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Similarity Solution for Fractional Diffusion Equation by Jun-Sheng Duan, Ai-Ping Guo, Wen-Zai Yun

“…Fractional diffusion equation in fractal media is an integropartial differential equation parametrized by fractal Hausdorff dimension and anomalous diffusion exponent. …”
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A Generalized Solow-Swan Model by Donghan Cai, Hui Ye, Longfei Gu

“…By introducing generalized exogenous variables into the classical Solow-Swan model, we obtain a nonautomatic differential equation. It is proved that the solution of the differential equation is asymptotically stable if the generalized exogenous variables converge and does not converge when one of the generalized exogenous variables persistently oscillates.…”
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Pulse Dynamics in a Bistable Reaction-Diffusion System with Chemotaxis by Satoshi Kawaguchi

“…We derive the ordinary differential equation of interfaces by applying the multiple scales method to the reaction-diffusion system for examining the effect of the chemotaxis on pulse dynamics in one dimension. …”
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The Analysis of Contour Integrals by Tanfer Tanriverdi, JohnBryce Mcleod

“…For any 𝑛, the contour integral 𝑦=cosh𝑛+1𝑥∮𝐶(cosh(𝑧𝑠)/(sinh𝑧−sinh𝑥)𝑛+1𝑑𝑧,𝑠2=−𝜆, is associated with differential equation 𝑑2𝑦(𝑥)/𝑑𝑥2+(𝜆+𝑛(𝑛+1)/cosh2𝑥)𝑦(𝑥)=0. …”
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Numerical Solution of Uncertain Beam Equations Using Double Parametric Form of Fuzzy Numbers by Smita Tapaswini, S. Chakraverty

“…Using the single parametric form, the fuzzy beam equation is converted first to an interval-based fuzzy differential equation. Next, this differential equation is transformed to crisp form by applying double parametric form of fuzzy number. …”
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Fixed Points for Multivalued Suzuki Type (θ,R)-Contraction Mapping with Applications by Mujahid Abbas, Hira Iqbal, Adrian Petrusel

“…As an application of our results, we obtain a homotopy result, proving the existence of a solution for a second-order differential equation and for a first-order fractional differential equation.…”
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Well-posedness of the difference schemes of the high order of accuracy for elliptic equations by Allaberen Ashyralyev, Pavel E. Sobolevskiĭ

“…It is well known the differential equation −u″(t)+Au(t)=f(t)(−∞<t<∞) in a general Banach space E with the positive operator A is ill-posed in the Banach space C(E)=C((−∞,∞),E) of the bounded continuous functions ϕ(t) defined on the whole real line with norm ‖ϕ‖C(E)=sup⁡−∞<t<∞‖ϕ(t)‖E. …”
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Asian Option Pricing with Transaction Costs and Dividends under the Fractional Brownian Motion Model by Yan Zhang, Di Pan, Sheng-Wu Zhou, Miao Han

“…The pricing problem of geometric average Asian option under fractional Brownian motion is studied in this paper. The partial differential equation satisfied by the option’s value is presented on the basis of no-arbitrage principle and fractional formula. …”
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Axially Symmetric-dS Solution in Teleparallel f(T) Gravity Theories by Gamal G. L. Nashed

“…Using this tetrad, we get a differential equation from the scalar torsion T=TαμνSαμν. …”
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Structural Parameter Identification of Fixed End Beams by Inverse Method Using Measured Natural Frequencies by T. Türker, A. Bayraktar

“…The solution of free bending transverse vibration of the beam is obtained by solving the differential equation motion of Bernoulli-Euler beam. By introducing the natural frequencies from experimental measurements into the solution of differential equation, the structural parameters of the fixed end beam are calculated.…”
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Propagation of Shear Horizontal Wave at Magneto-Electro-Elastic Structure Subjected to Mechanically Imperfect Interface by Anandakrishnan Akshaya, Santosh Kumar, Kulandhaivel Hemalatha

“…This involves initially transforming the partial differential equation into an ordinary differential equation through basic variable separation and the ordinary differential equation is solved by WKB approximation technique. …”
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On Bending of Bernoulli-Euler Nanobeams for Nonlocal Composite Materials by Luciano Feo, Rosa Penna

“…Unlike standard treatments, a second-order differential equation of nonlocal equilibrium elastic is integrated in terms of transverse displacements and equilibrated bending moments. …”
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Viscosity Solution of Mean-Variance Portfolio Selection of a Jump Markov Process with No-Shorting Constraints by Moussa Kounta

“…In this situation the Hamilton-Jacobi-Bellman (HJB) equation of the value function of the auxiliary problem becomes a coupled system of backward stochastic partial differential equation. In fact, the value function V often does not have the smoothness properties needed to interpret it as a solution to the dynamic programming partial differential equation in the usual (classical) sense; however, in such cases V can be interpreted as a viscosity solution. …”
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A Legendre Wavelet Spectral Collocation Method for Solving Oscillatory Initial Value Problems by A. Karimi Dizicheh, F. Ismail, M. Tavassoli Kajani, Mohammad Maleki

“…In this paper, we propose an iterative spectral method for solving differential equations with initial values on large intervals. …”
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On the Possibility of the Jerk Derivative in Electrical Circuits by J. F. Gómez-Aguilar, J. Rosales-García, R. F. Escobar-Jiménez, M. G. López-López, V. M. Alvarado-Martínez, V. H. Olivares-Peregrino

“…For γ=3/2, the system is described by a third-order differential equation with frequency ω~ω03/2, and assuming γ=2 the dynamics are described by a fourth differential equation for jerk dynamics with frequency ω~ω02.…”
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Investigating wave solutions in coupled nonlinear Schrödinger equation: insights into bifurcation, chaos, and sensitivity by Adil Jhangeer, Abdallah M. Talafha, Ariana Abdul Rahimzai, Lubomír Říha

“…The transformation of the coupled partial differential equation into ordinary differential equation is achieved by utilizing a complex wave variable. …”
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