Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions by Bashir Ahmad, Juan J. Nieto

“…The contraction mapping principle and Krasnoselskii's fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space.…”
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A Fractional Model for the Dynamics of Smoking Tobacco Using Caputo–Fabrizio Derivative by Belaynesh Melkamu, Benyam Mebrate

“…The solution of the proposed model, which is carried out using a fixed-point theorem and an iterative method, exists and is unique. …”
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Uniqueness and Asymptotic Behavior of Positive Solutions for a Fractional-Order Integral Boundary Value Problem by Min Jia, Xin Liu, Xuemai Gu

“…Our analysis relies on Schauder's fixed-point theorem and upper and lower solution method.…”
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Null Controllability of a Nonlinear Age Structured Model for a Two-Sex Population by Amidou Traoré, Okana S. Sougué, Yacouba Simporé, Oumar Traoré

“…Our method uses first an observability inequality related to the adjoint of an auxiliary system, a null controllability of the linear auxiliary system, and after Kakutani’s fixed-point theorem.…”
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Existence of Concave Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation with p-Laplacian Operator by Jinhua Wang, Hongjun Xiang, ZhiGang Liu

“…We consider the existence and multiplicity of concave positive solutions for boundary value problem of nonlinear fractional differential equation with p-Laplacian operator D0+γ(ϕp(D0+αu(t)))+f(t,u(t),D0+ρu(t))=0, 0<t<1, u(0)=u′(1)=0, u′′(0)=0, D0+αu(t)|t=0=0, where 0<γ<1, 2<α<3, 0<ρ⩽1, D0+α denotes the Caputo derivative, and f:[0,1]×[0,+∞)×R→[0,+∞) is continuous function, ϕp(s)=|s|p-2s, p>1,  (ϕp)-1=ϕq,  1/p+1/q=1. By using fixed point theorem, the results for existence and multiplicity of concave positive solutions to the above boundary value problem are obtained. …”
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Optimal individual strategies for influenza vaccines with imperfect efficacy and durability of protection by Francesco Salvarani, Gabriel Turinici

“…We prove the existence of a Nash equilibrium by Kakutani's fixed point theorem in the context of non-persistent immunity. …”
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On the existence of solutions to fractional differential equations involving Caputo q-derivative in Banach spaces by Isra Al-Shbeil, Houari Bouzid, Benali Abdelkader, Alina Alp Lupas, Mohammad Esmael Samei, Reem K. Alhefthi

“…We analyze the existence and uniqueness of solutions to the multi-point nonlinear BVPs base on fixed point theory, including fixed point theorem of Banach, Leray-nonlinear Schauder's alternative, and Leray-degree Schauder's theory. …”
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Positive and Nondecreasing Solutions to an m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation by I. J. Cabrera, J. Harjani, K. B. Sadarangani

“…Our analysis relies on a fixed point theorem in partially ordered sets. Some examples are also presented to illustrate the main results.…”
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Multiple Positive Solutions for a Coupled System of p-Laplacian Fractional Order Two-Point Boundary Value Problems by K. R. Prasad, B. M. B. Krushna

“…This paper establishes the existence of at least three positive solutions for a coupled system of p-Laplacian fractional order two-point boundary value problems, D0+β1(ϕp(D0+α1u(t)))=f1(t,u(t),v(t)), t∈(0,1), D0+β2(ϕp(D0+α2v(t)))=f2(t,u(t),v(t)), t∈(0,1), u(0)=D0+q1u(0)=0, γu(1)+δD0+q2u(1)=0, D0+α1u(0)=D0+α1u(1)=0, v(0)=D0+q1v(0)=0, γv(1)+δD0+q2v(1)=0, D0+α2v(0)=D0+α2v(1)=0, by applying five functionals fixed point theorem.…”
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On a Memristor-Based Hyperchaotic Circuit in the Context of Nonlocal and Nonsingular Kernel Fractional Operator by Shahram Rezapour, Chernet Tuge Deressa, Sina Etemad

“…A five-dimensional memristor-based circuit in the context of a nonlocal and nonsingular fractional derivative is considered for analysis. The Banach fixed point theorem and contraction principle are utilized to verify the existence and uniqueness of the solution of the five-dimensional system. …”
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The Existence of Positive Solutions for Boundary Value Problem of the Fractional Sturm-Liouville Functional Differential Equation by Yanan Li, Shurong Sun, Zhenlai Han, Hongling Lu

“…By means of the Guo-Krasnoselskii fixed point theorem and the fixed point index theorem, some positive solutions are obtained, respectively. …”
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Global Positive Periodic Solutions of Generalized n-Species Gilpin-Ayala Delayed Competition Systems with Impulses by Zhenguo Luo, Liping Luo, Jianhua Huang, Binxiang Dai

“…By applying the Krasnoselskii fixed-point theorem in a cone of Banach space, we derive some verifiable necessary and sufficient conditions for the existence of positive periodic solutions of the previously mentioned. …”
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Existence of periodic traveling wave solution to the forced generalized nearly concentric Korteweg-de Vries equation by Kenneth L. Jones, Xiaogui He, Yunkai Chen

“…The Schauder's fixed point theorem is then used to prove the existence of nonconstant solutions to the integral equations. …”
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Some Existence, Uniqueness, and Stability Results for a Class of <i>ϑ</i>-Fractional Stochastic Integral Equations by Fahad Alsharari, Raouf Fakhfakh, Omar Kahouli, Abdellatif Ben Makhlouf

“…This paper focuses on the existence and uniqueness of solutions for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϑ</mi></semantics></math></inline-formula>-fractional stochastic integral equations (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϑ</mi></semantics></math></inline-formula>-FSIEs) using the Banach fixed point theorem (BFPT). We explore the Ulam–Hyers stability (UHS) of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϑ</mi></semantics></math></inline-formula>-FSIEs through traditional methods of stochastic calculus and the BFPT. …”
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Three Positive Periodic Solutions to Nonlinear Neutral Functional Differential Equations with Parameters on Variable Time Scales by Yongkun Li, Chao Wang

“…Using two successive reductions: B-equivalence of the system on a variable time scale to a system on a time scale and a reduction to an impulsive differential equation and by Leggett-Williams fixed point theorem, we investigate the existence of three positive periodic solutions to the nonlinear neutral functional differential equation on variable time scales with a transition condition between two consecutive parts of the scale (d/dt)(x(t)+c(t)x(t-α))=a(t)g(x(t))x(t)-∑j=1nλjfj(t,x(t-vj(t))), (t,x)∈T0(x),Δt|(t,x)∈S2i=Πi1(t,x)-t, Δx|(t,x)∈S2i=Πi2(t,x)-x, where Πi1(t,x)=t2i+1+τ2i+1(Πi2(t,x)) and Πi2(t,x)=Bix+Ji(x)+x,  i=1,2,….  …”
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Discrete Derivative Nonlinear Schrödinger Equations by Dirk Hennig, Jesús Cuevas-Maraver

“…In fact, we prove the existence of solitary TWs, facilitating Schauder’s fixed-point theorem. For the damped forward expansive ddNLS we demonstrate that there exists such a balance of dissipation so that solitary stationary modes exist.…”
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Computational Study of a Fractional-Order HIV Epidemic Model with Latent Phase and Treatment by Sana Abdulkream Alharbi, Nada A. Almuallem

“…We derive some results from the fixed-point theorem and Ulam–Hyers stability. Ultimately, the obtained numerical simulation results are in agreement with the analytical outcomes obtained from the model analysis. …”
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On the 75th birth anniversary of Marat Mirzaevich Arslanov by I.Sh. Kalimullin, V.L. Selivanov

“…Arslanov that gave him international fame, is Arslanov's fixed point theorem (also known as Arslanov's completeness criterion), which was first formulated and proved by M.M. …”
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Existence and stability results in a fractional optimal control model for dengue and two-strains of salmonella typhi by Anum Aish Buhader, Mujahid Abbas, Mudassar Imran, Andrew Omame

“…Existence, uniqueness and stability of the model are proved by implementing Arzela Ascoli’s theorem, Banach fixed point theorem and Hyers-Ulam stability criteria, respectively. …”
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The Existence of Positive Solutions for a Fourth-Order Difference Equation with Sum Form Boundary Conditions by Yanping Guo, Xuefei Lv, Yude Ji, Yongchun Liang

“…We consider the fourth-order difference equation: Δ(z(k+1)Δ3u(k-1))=w(k)f(k,u(k)),  k∈{1,2,…,n-1} subject to the boundary conditions: u(0)=u(n+2)=∑i=1n+1g(i)u(i), aΔ2u(0)-bz(2)Δ3u(0)=∑i=3n+1h(i)Δ2u(i-2), aΔ2u(n)-bz(n+1)Δ3u(n-1)=∑i=3n+1h(i)Δ2u(i-2), where a,b>0 and Δu(k)=u(k+1)-u(k) for k∈{0,1,…,n-1},  f:{0,1,…,n}×[0,+∞)→[0,+∞) is continuous. h(i) is nonnegative i∈{2,3,…,n+2}; g(i) is nonnegative for i∈{0,1,…,n}. Using fixed point theorem of cone expansion and compression of norm type and Hölder’s inequality, various existence, multiplicity, and nonexistence results of positive solutions for above problem are derived, which extends and improves some known recent results.…”
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