On Oscillations of Solutions of Third-Order Dynamic Equation by Gro Hovhannisyan

“…We are proving the new oscillation theorems for the solutions of third-order linear nonautonomous differential equation with complex coefficients. In the case of real coefficients we derive the oscillation criterion that is invariant with respect to the adjoint transformation. …”
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Approximate controllability of neutral functional differential system with unbounded delay by Jong Yeoul Park, Sang Nam Kang

“…We consider a class of control systems governed by the neutral functional differential equation with unbounded delay and study the approximate controllability of the system. …”
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An oriented coincidence index for nonlinear Fredholm inclusions with nonconvex-valued perturbations

“…An example arising in the study of a mixed system, consisting of a first-order implicit differential equation and a differential inclusion, is given.…”
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About the location of some quasipolinomial roots by Donatas Švitra, Ingrida Sirvydaitė

“…The same research is carried out for a differential equation with delay of neutral type appearing in mathematical ecology. …”
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The Second Kummer Function with Matrix Parameters and Its Asymptotic Behaviour by Georg Wehowar, Erika Hausenblas

“…Further, we provide a closed form of a solution of a Weber matrix differential equation and give a representation using the second Kummer function.…”
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Uniqueness of semilinear elliptic inverse problem by Chaochun Qu, Ping Wang

“…We consider the uniqueness of the inverse problem for a semilinear elliptic differential equation with Dirichlet condition. The necessary and sufficient condition of unique solution is obtained. …”
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Viscosity Solutions and American Option Pricing in a Stochastic Volatility Model of the Ornstein-Uhlenbeck Type by Alexandre F. Roch

“…We characterize the value of such derivatives as the unique viscosity solution of an integral-partial differential equation when the payoff function satisfies a Lipschitz condition.…”
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Image Texture Analysis and Edge Detection Algorithm Based on Anisotropic Diffusion Equation by Xiaoqin Li

“…This paper uses partial differential equation image processing techniques to establish image texture analysis models based on nonlinear anisotropic diffusion equations for image denoising, image segmentation, and image decomposition. …”
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New exact soliton wave solutions appear in optical fibers with Sardar sub equation and new auxiliary equation techniques by Umair Asghar, Muhammad Imran Asjad, Yasser Salah Hamed, Ali Akgul, Murad Khan Hassani

“…These methods are applied to derive a wide range of soliton solutions for nonlinear partial differential equations. By transforming the original partial differential equation into an ordinary differential equation using an appropriate transformation, various types of solitary wave solutions are obtained. …”
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Well-Testing Model for Dual-Porosity Reservoir considering Stress-Sensitivity and Elastic Outer Boundary Condition by Song Chol Kim, Song Guk Han, Yong Il Song, Jin Sim Kim, Myong Gun Hong

“…To solve this model, a nonlinear partial differential equation is changed into a linear form of a partial differential equation by introducing an effective well radius and applying Pedrosa’s transformation and perturbation transformation. …”
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The Local Stability of Solutions for a Nonlinear Equation by Haibo Yan, Ls Yong

“…The approach of Kruzkov’s device of doubling the variables is applied to establish the local stability of strong solutions for a nonlinear partial differential equation in the space L1(R) by assuming that the initial value only lies in the space L1(R)∩L∞(R).…”
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Bounds of Solutions of Integrodifferential Equations by Zdeněk Šmarda

“…Some new integral inequalities are given, and bounds of solutions of the following integro-differential equation are determined: x'(t)-F(t,x(t),∫0tk(t,s,x(t),x(s))ds)=h(t), x(0)=x0, where h:R+→R, k:R+2×R2→R, F:R+×R2→R are continuous functions, R+=[0,∞).…”
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Approximation of Analytic Functions by Bessel's Functions of Fractional Order by Soon-Mo Jung

“…We will solve the inhomogeneous Bessel's differential equation x2y″(x)+xy′(x)+(x2-ν2)y(x)=∑m=0∞amxm, where ν is a positive nonintegral number and apply this result for approximating analytic functions of a special type by the Bessel functions of fractional order.…”
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On oscillation of a food-limited population model with time delay by Leonid Berezansky, Elena Braverman

“…For a scalar nonlinear delay differential equation Ṅ(t) = r(t)N(t)(K − N(h(t)))/(K + s(t)N(g(t))),r(t) ≥ 0, h(t) ≤ t, g(t) ≤ t and some generalizations of this equation, we establish explicit oscillation and nonoscillation conditions. …”
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Formulation and Solution of th-Order Derivative Fuzzy Integrodifferential Equation Using New Iterative Method with a Reliable Algorithm by A. A. Hemeda

“…The analysis is accompanied by numerical examples which confirm efficiency and power of this method in solving fuzzy integro-differential equations.…”
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Existence and Uniqueness of Solutions for a Fractional Order Antiperiodic Boundary Value Problem with a p-Laplacian Operator by Ruihui Huang

“…We study the existence and uniqueness of solutions for a class of antiperiodic boundary value problems of the fractional differential equation with a p-Laplacian operator. Based on the Leray-Schauder nonlinear alternative, several sufficient conditions of the existence and uniqueness of solution of the above problem are established. …”
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Approximate Solutions of Delay Parabolic Equations with the Dirichlet Condition by Deniz Agirseven

“…Finite difference and homotopy analysis methods are used for the approximate solution of the initial-boundary value problem for the delay parabolic partial differential equation with the Dirichlet condition. The convergence estimates for the solution of first and second orders of difference schemes in Hölder norms are obtained. …”
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Pricing of European Currency Options with Uncertain Exchange Rate and Stochastic Interest Rates by Xiao Wang

“…Suppose that the interest rates obey stochastic differential equations, while the exchange rate follows an uncertain differential equation; this paper proposes a new currency model. …”
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Weak Solutions for a p-Laplacian Antiperiodic Boundary Value Problem with Impulsive Effects by Keyu Zhang, Jiafa Xu, Wei Dong

“…By virtue of variational method and critical point theory, we will investigate the existence of weak solutions for a p-Laplacian impulsive differential equation with antiperiodic boundary conditions.…”
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A Nonlinear Implicit Fractional Equation with Caputo Derivative by Ameth Ndiaye

“…In this paper, we study a nonlinear implicit differential equation with initial conditions. The considered problem involves the fractional Caputo derivatives under some conditions on the order. …”
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