Positive Solutions of Fractional Differential Equation with -Laplacian Operator by Teng Ren, Xiaochun Chen

“…In this paper, we study an ecological model arising from ecological economics by mathematical method, that is, study the existence of positive solutions for the fractional differential equation with -Laplacian operator , , , , , and , where are the standard Riemann-Liouville derivatives, -Laplacian operator is defined as , and the nonlinearity may be singular at both and By finding more suitable upper and lower solutions, we omit some key conditions of some existing works, and the existence of positive solution is established.…”
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The Hyperorder of Solutions of Second-Order Linear Differential Equations by Guowei Zhang

“…We prove that the hyperorder of every nontrivial solution of homogenous linear differential equations of type and nonhomogeneous equation of type is one, where are entire functions of order less than one, improving the previous results of Chen, Wang, and Laine.…”
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Stability Analysis of Distributed Order Fractional Differential Equations by H. Saberi Najafi, A. Refahi Sheikhani, A. Ansari

“…We analyze the stability of three classes of distributed order fractional differential equations (DOFDEs) with respect to the nonnegative density function. …”
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On the Hyers-Ulam Stability of Differential Equations of Second Order by Qusuay H. Alqifiary, Soon-Mo Jung

“…By using of the Gronwall inequality, we prove the Hyers-Ulam stability of differential equations of second order with initial conditions.…”
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Rapid Convergence of Approximate Solutions for Fractional Differential Equations by Xiran Wu, Junyan Bao, Yufeng Sun

“…In this paper, we develop a generalized quasilinearization technique for a class of Caputo’s fractional differential equations when the forcing function is the sum of hyperconvex and hyperconcave functions of order m (m≥0), and we obtain the convergence of the sequences of approximate solutions by establishing the convergence of order k (k≥2).…”
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Existence for Certain Systems of Nonlinear Fractional Differential Equations by Zhaowen Zheng, Xiujuan Zhang, Jing Shao

“…By establishing a comparison result and using the monotone iterative technique, combining with the method of upper and lower solutions, the existence of solutions for systems of nonlinear fractional differential equations is considered. An example is given to demonstrate the applicability of our results.…”
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Analysis of Fractional Differential Equations with the Help of Different Operators by Naveed Iqbal, Moteb Fheed Saad Al Harbi, Saleh Alshammari, Shamsullah Zaland

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Oscillation of Third-Order Neutral Delay Differential Equations by Tongxing Li, Chenghui Zhang, Guojing Xing

“…The purpose of this paper is to examine oscillatory properties of the third-order neutral delay differential equation [a(t)(b(t)(x(t)+p(t)x(σ(t)))′)′]′+q(t)x(τ(t))=0. …”
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On the Cauchy problem for a degenerate parabolic differential equation by Ahmed El-Fiky

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Stability of Nonlinear Neutral Stochastic Functional Differential Equations by Minggao Xue, Shaobo Zhou, Shigeng Hu

“…Neutral stochastic functional differential equations (NSFDEs) have recently been studied intensively. …”
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Perturbed Galerkin Method for Solving Integro-Differential Equations by K. Issa, J. Biazar, T. O. Agboola, T. Aliu

“…In this paper, perturbed Galerkin method is proposed to find numerical solution of an integro-differential equations using fourth kind shifted Chebyshev polynomials as basis functions which transform the integro-differential equation into a system of linear equations. …”
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Eigenvalue of Fractional Differential Equations with p-Laplacian Operator by Wenquan Wu, Xiangbing Zhou

“…By constructing upper and lower solutions, the existence of positive solutions for the eigenvalue problem of fractional differential equation is established.…”
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The Existence and Uniqueness of a Class of Fractional Differential Equations by Zhanbing Bai, Sujing Sun, YangQuan Chen

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Positive Solutions for Coupled Nonlinear Fractional Differential Equations by Wenning Liu, Xingjie Yan, Wei Qi

“…We consider the existence of positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary values. Assume the nonlinear term is superlinear in one equation and sublinear in the other equation. …”
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Numerical solution of second order ordinary differential equations by Ayokunle Tadema

“…In this article, we introduce the Milne-Simpson predictor-corrector technique (MS) and the fourth-order Adam-Bashforth-Moulton predictor-corrector method (ADM) for solving second-order initial value problems (IVPs) of ordinary differential equations.Both methods are highly efficient and particularly suitable for addressing IVPs. …”
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The Conical Radial Basis Function for Partial Differential Equations by J. Zhang, F. Z. Wang, E. R. Hou

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Impulsive Multiorders Riemann-Liouville Fractional Differential Equations by Weera Yukunthorn, Sotiris K. Ntouyas, Jessada Tariboon

“…Impulsive multiorders fractional differential equations are studied. Existence and uniqueness results are obtained for first- and second-order impulsive initial value problems by using Banach’s fixed point theorem in an appropriate weighted space. …”
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On point-dissipative systems of differential equations with quadratic nonlinearity by Anile K. Bose, Alan S. Cover, James A. Reneke

“…The system x′=Ax+f(x) of nonlinear vector differential equations, where the nonlinear term f(x) is quadratic with orthogonality property xTf(x)=0 for all x, is point-dissipative if uTAu<0 for all nontrivial zeros u of f(x).…”
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Nonoscillation theorems for functional differential equations of arbitrary order by John R. Graef, Myron K. Grammatikopoulos, Yuichi Kitamura, Takasi Kusano, Hiroshi Onose, Paul W. Spikes

“…The authors give sufficient conditions for all oscillatory solutions of a sublinear forced higher order nonlinear functional differential equation to converge to zero. They then prove a nonoscillation theorem for such equations. …”
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Approximate Boundary Controllability for Semilinear Delay Differential Equations by Lianwen Wang

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