Existence and Numerical Simulation of Solutions for Fractional Equations Involving Two Fractional Orders with Nonlocal Boundary Conditions by Jing Zhao, Peifen Lu, Yiliang Liu

“…We study a boundary value problem for fractional equations involving two fractional orders. …”
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Global Strong Solution to the Density-Dependent 2-D Liquid Crystal Flows by Yong Zhou, Jishan Fan, Gen Nakamura

“…The initial-boundary value problem for the density-dependent flow of nematic crystals is studied in a 2-D bounded smooth domain. …”
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On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs-Type Inequality by G. A. Chechkin, Yu. O. Koroleva, L.-E. Persson, P. Wall

“…In this paper, we construct and verify the asymptotic expansion for the spectrum of a boundary-value problem in a unit circle periodically perforated along the boundary. …”
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A Mixed Finite Element Formulation for the Conservative Fractional Diffusion Equations by Suxiang Yang, Huanzhen Chen

“…We consider a boundary-value problem of one-side conservative elliptic equation involving Riemann-Liouville fractional integral. …”
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New Exact Traveling Wave Solutions of Fractional Time Coupled Nerve Fibers via Two New Approaches by Saud Owyed

“…The equation and the solution methods have free parameters which help to make the obtained solutions are dynamics and more readable for dealing with fractional parameter and the initial and boundary value problem. As a result, various new exact soliton solutions for the considered model are derived which include the hyperbolic, rational, and trigonometric functions, and other solutions are obtained. …”
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Results on non local impulsive implicit Caputo-Hadamard fractional differential equations by K. Venkatachalam, M. Sathish Kumar, P. Jayakumar

“…The results for a new modeling integral boundary value problem using Caputo-Hadamard impulsive implicit fractional differential equations with Banach space are investigated, along with the existence and uniqueness of solutions. …”
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Construction of a Class of Copula Using the Finite Difference Method by Remi Guillaume Bagré, Frédéric Béré, Vini Yves Bernadin Loyara

“…In this paper, we present a method that allows us to obtain a class of copula as a solution to a boundary value problem. For this, we use the finite difference method which is a common technique for finding approximate solutions of partial differential equations which consists in solving a system of relations (numerical scheme) linking the values of the unknown functions at certain points sufficiently close to each other.…”
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An Iterative Algorithm for Solving n-Order Fractional Differential Equation with Mixed Integral and Multipoint Boundary Conditions by Jingjing Tan, Xinguang Zhang, Lishan Liu, Yonghong Wu

“…In this paper, we consider the iterative algorithm for a boundary value problem of n-order fractional differential equation with mixed integral and multipoint boundary conditions. …”
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Existence of Positive Solution for BVP of Nonlinear Fractional Differential Equation by Jun-Rui Yue, Jian-Ping Sun, Shuqin Zhang

“…We consider the following boundary value problem of nonlinear fractional differential equation: (CD0+αu)(t)=f(t,u(t)),  t∈[0,1],  u(0)=0,   u′(0)+u′′(0)=0,  u′(1)+u′′(1)=0, where α∈(2,3] is a real number,  CD0+α denotes the standard Caputo fractional derivative, and f:[0,1]×[0,+∞)→[0,+∞) is continuous. …”
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Nonexistence of Global Solutions for Coupled System of Pseudoparabolic Equations with Variable Exponents and Weak Memories by Kh. Zennir, H. Dridi, S. Alodhaibi, S. Alkhalaf

“…The nonsolvability of boundary value problem for damped pseudoparabolic differential equations with variable exponents is investigated. …”
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Boltzmann’s Six-Moment One-Dimensional Nonlinear System Equations with the Maxwell-Auzhan Boundary Conditions by A. Sakabekov, Y. Auzhani

“…In order to obtain a priori estimation of the initial and boundary value problem for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations we get the integral equality and then use the spherical representation of vector. …”
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Solvability for a New Class of Moore-Gibson-Thompson Equation with Viscoelastic Memory, Source Terms, and Integral Condition by Salah Mahmoud Boulaaras, Abdelbaki Choucha, Djamel Ouchenane, Asma Alharbi, Mohamed Abdalla, Bahri Belkacem Cherif

“…This paper deals with the existence and uniqueness of solutions of a new class of Moore-Gibson-Thompson equation with respect to the nonlocal mixed boundary value problem, source term, and nonnegative memory kernel. …”
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On Bending of Bernoulli-Euler Nanobeams for Nonlocal Composite Materials by Luciano Feo, Rosa Penna

“…An innovative methodology, characterized by a lowering in the order of governing differential equation, is adopted in the present manuscript in order to solve the boundary value problem of a nanobeam under flexure. 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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Existence and Uniqueness of Positive and Bounded Solutions of a Discrete Population Model with Fractional Dynamics by J. E. Macías-Díaz

“…Positive and bounded initial-boundary data are imposed on a closed and bounded domain, and a fully discrete form of this fractional initial-boundary-value problem is provided next using fractional centered differences. …”
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On New High Order Quasilinearization Approaches to the Nonlinear Model of Catalytic Reaction in a Flat Particle by S. S. Motsa, O. D. Makinde, S. Shateyi

“…A novel computational approach known as pseudospectral quasilinearization (SQLM) is employed to tackle the two-point boundary value problem describing the reactivity behaviour of porous catalyst particles subject to both internal mass concentration gradients and temperature gradients, in endothermic or exothermic catalytic reactions. …”
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New Existence Results for Nonlinear Fractional Integrodifferential Equations by Lahcen Ibnelazyz, Karim Guida, Khalid Hilal, Said Melliani

“…This paper discusses a boundary value problem of nonlinear fractional integrodifferential equations of order 1<α≤2 and 1<β≤2 and boundary conditions of the form x0=x1=Dcβx1=Dcβx0=0. …”
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Complexity of Computation of Dominating Sets in Geo-Mathmetics Algorithm : A Review by Şakir Işleyen

“…The graph in graph is 2: The histogram is an example that illustrates the histogram.Keywords— Boundary Value Problem, Convergence of the Method, Cubic Order, Finite Difference Method, Non-uniform Step Length. …”
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Similarity Solution for High Weissenberg Number Flow of Upper-Convected Maxwell Fluid on a Linearly Stretching Sheet by Meysam Mohamadali, Nariman Ashrafi

“…Numerical solutions to the resulting boundary value problem are obtained using an efficient shooting technique in conjunction with a variable stepping method for different values of pressure gradients. …”
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An Existence Theorem for a Nonlocal Global Pandemic Model for Insect-Borne Diseases by John R. Cannon, Daniel J. Galiffa

“…This transformation amounts to a nonlocal boundary value problem on the unit sphere and therefore can be interpreted as a global pandemic model for insect-borne diseases. …”
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On the global well-posedness and exponential stability of 3D heat conducting incompressible Navier-Stokes equations with temperature-dependent coefficients and vacuum by Jianxia He, Qingyan Li

“…This paper focuses on investigating the initial-boundary value problem of incompressible heat conducting Navier-Stokes equations with variable coefficients over bounded domains in $ \mathbb{R}^3 $, where the viscosity coefficient and heat conduction coefficient are powers of temperature. …”
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