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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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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Accuracy, Robustness, and Efficiency of the Linear Boundary Condition for the Black-Scholes Equations by Darae Jeong, Seungsuk Seo, Hyeongseok Hwang, Dongsun Lee, Yongho Choi, Junseok Kim

“…We briefly review and investigate the performance of various boundary conditions such as Dirichlet, Neumann, linear, and partial differential equation boundary conditions for the numerical solutions of the Black-Scholes partial differential equation. …”
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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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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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Natural Frequency Analysis based on RV Reducer Theory Model by Yueming Zhang, Bin Shao, Shuting Ji

“…Taking RV-320E gear reducer as the research object and considering tangential degrees of freedom of crank shaft and cycloid wheel rotation motion，the 16 degrees of freedom dynamic model of RV gear reducer is established by centralized mass method. The dynamics differential equation of the system is established by Newton's second law and the differential equation of fixed axis rotation，and the natural frequency of the system is calculated. …”
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Approximation of Analytic Functions by Chebyshev Functions by Soon-Mo Jung, Themistocles M. Rassias

“…We solve the inhomogeneous Chebyshev's differential equation and apply this result for approximating analytic functions by the Chebyshev functions.…”
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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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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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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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Analysing nonlinear oscillation and chaos using fundamental-wave balance principle by HUANG Bing-hua, HUANG Xin-min, WEI Shan-ge

“…The universality of the conclusion can be spread to third-order nonlinear differential equation. It is expounded that a differential equation possessing multiple periodic solutions is the important reason of generating chaotic oscillation. …”
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Modeling Method and Inherent Characteristic Analysis of Cycloid Pin Gear Transmission by Xueping Song, Aibin Bi, Bowen Lu

“…Considering the eccentric motion of cycloid and the influence of time-varying stiffness， backlash and transmission error of cycloid and pin gear， the differential equation of motion of the system is obtained by Lagrange method. …”
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Theory of Frequency Captured of Eccentric Rotor by Vibration Environment with Same Direction by Su Ming, Li Rong, Xie Zhiping, Zheng Jiming

“…An integral mean method with small parameters and periodic coefficient (IMM-SPPC) is proposed, which converts the relative motion of the electrically driven eccentric rotor and the vibration environment into a second-order periodic coefficient differential equation. Through the calculation of the equilibrium point of the second-order periodic coefficient differential equation and the study of its stability, the synchronization criterion and the stability criterion of the eccentric rotor and the vibration environment are deduced. …”
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Unified study on characteristic spectrum representation of signals and spectral decomposition for stationary random signals by Hongyu WANG, Tianshuang QIU

“…By using the relations among the differential operators, the integral operator and the Green's function of the characteristic differential equation, the inverse relationship between the Hermitian differential operator and the Hermitian integral operator were given, the characteristic differential equation and corresponding characteristic integral equation were demonstrated, and the spectral representations of both Hermitian differential and integral operators and the general spectral representations for both operators were provided. …”
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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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Analysis of Torsional Vibration Characteristic for the Crown Gear Coupling of EMU by Shi Zhenqiang, Xia Qinghua, Zhang Dezhi, Zhang Dianlong, Zhu Changping

“…According to the structural characteristics and operating conditions of the crown gear coupling of EMU,the torsional vibration system mechanical model of the crown gear coupling is established by using lumped parameter method,and the differential equation of torsional vibration is established. …”
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Analysis of Thermoelastic Coupling Vibration of Friction Plate in Friction Clutch by Yongqiang Yang, Zhongmin Wang, Yongqin Wang

“…The differential equation and the boundary condition are discretized by the differential quadrature method. …”
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1:2 PARAMETRIC RESONANCE OF MICRO-BEAN SYSTEM SUBJECTED TO NARROW-BAND RANDOM EXCITATION by YANG ZhiAn, ZHAO KaiYuan

“…To study the parametric resonance of series circuit and micro-beam coupling system subjected to the narrow-band random excitation, the stochastic differential equation of the micro-beam system subjected to narrow-band excitation is established. …”
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