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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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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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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Multiple Positive Solutions of Singular Nonlinear Sturm-Liouville Problems with Carathéodory Perturbed Term by Yuefeng Han, Xinguang Zhang, Lishan Liu, Yonghong Wu

“…By employing a well-known fixed point theorem, we establish the existence of multiple positive solutions for the following fourth-order singular differential equation Lu=p(t)f(t,u(t),u′′(t))-g(t,u(t),u′′(t)),0<t<1,α1u(0)-β1u'(0)=0,γ1u(1)+δ1u'(1)=0,α2u′′(0)-β2u′′′(0)=0,γ2u′′(1)+δ2u′′′(1)=0, with αi,βi,γi,δi≥0 and βiγi+αiγi+αiδi>0,    i=1,2, where L denotes the linear operator Lu:=(ru′′′)'-qu′′,r∈C1([0,1],(0,+∞)), and q∈C([0,1],[0,+∞)). …”
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Numerical Algorithm for Coupled Fixed Points in Normed Spaces with Applications to Fractional Differential Equations and Economics by Lifang Guo, Salha Alshaikey, Abeer Alshejari, Muhammad Din, Umar Ishtiaq

“…Furthermore, we introduce the idea of a coupled interpolative enriched cyclic Reich–Rus–Ćirić operator and establish the existence of a strongly coupled fixed-point theorem for this contraction. Finally, we provide an application to fractional differential equations to show the validity of the main result.…”
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Hybrid technique for multi-dimensional fractional diffusion problems involving Caputo–Fabrizio derivative by Surendar Kumar Yadav, Mridula Purohit, Murli Manohar Gour, Lokesh Kumar Yadav, Manvendra Narayan Mishra

“…The proposed approach combines the Shehu transformation (ST) with the Adomian decomposition method (ADM), employing Adomain polynomials to handle nonlinear terms. Fixed point theorem has been used to prove the uniqueness and existence of the solution of governing differential equation. …”
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Positive Solutions Depending on Parameters for a Nonlinear Fractional System with p-Laplacian Operators by Chen Yang, Xiaolin Zhu

“…We obtain the existence and uniqueness of positive solutions depending on parameters for the system by utilizing a recent fixed point theorem. Furthermore, an example is present to illustrate our main result.…”
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Multi-valued mappings on Pompeiu-Hausdorff fuzzy b-metric spaces and a common fixed point result by Noreddine Makran, Stojan N. Radenović

“…Additionally, a general common fixed point theorem for a pair of multi-valued mappings in Pompeiu-Hausdorff fuzzy b-metric spaces is investigated. …”
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Relational Almost (<i>ϕ</i>,<i>ψ</i>)-Contractions and Applications to Nonlinear Fredholm Integral Equations by Fahad M. Alamrani, Ebrahem A. Algehyne, Esmail Alshaban, Adel Alatawi, Hamid I. A. Mohammed, Faizan Ahmad Khan

“…In the course of the procedure, we also derive a related fixed point theorem for strict almost <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>ϕ</mi><mo>,</mo><mi>ψ</mi><mo>)</mo></mrow></semantics></math></inline-formula>-contraction. …”
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Exploring the solutions of tempered (κ,ϖ)-Hilfer hybrid implicit boundary value problem by Abdelkrim Salim, Sabri T.M. Thabet, Ava Sh. Rafeeq, Mohammad Esmael Samei, Imed Kedim, Miguel Vivas-Cortez

“…To derive the results, we employ Banach’s fixed point theorem, which facilitates the demonstration of the existence of solutions under certain contractive conditions. …”
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Discrete Fractional-Order Modeling of Recurrent Childhood Diseases Using the Caputo Difference Operator by Yasir A. Madani, Zeeshan Ali, Mohammed Rabih, Amer Alsulami, Nidal H. E. Eljaneid, Khaled Aldwoah, Blgys Muflh

“…The existence theory is established using Brouwer’s fixed-point theorem and the Banach contraction principle, providing a comprehensive mathematical foundation for the model. …”
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A Proposal for Revisiting Ćirić and Caristi Type Theorems in Metric Spaces by Belkassem Seddoug, Soumia Chaira, Karim Chaira

“…In this paper, we revisit the renowned fixed point theorems of Ćirić and Caristi. We propose some new fixed point theorems in a metric space with partial order. …”
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The Existence of Fixed Points for Nonlinear Contractive Maps in Metric Spaces with 𝑤-Distances by Hossein Lakzian, Ing-Jer Lin

“…Some fixed point theorems for (𝜑,𝜓,𝑝)-contractive maps and (𝜑,𝑘,𝑝)-contractive maps on a complete metric space are proved. …”
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