Notes on Local and Nonlocal Intuitionistic Fuzzy Fractional Boundary Value Problems with Caputo Fractional Derivatives by Ali El Mfadel, Said Melliani, M’hamed Elomari

“…In this paper, we investigate the existence and uniqueness results of intuitionistic fuzzy local and nonlocal fractional boundary value problems by employing intuitionistic fuzzy fractional calculus and some fixed-point theorems. …”
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Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators by Dongyuan Liu, Zigen Ouyang, Huilan Wang

“…We consider the following state dependent boundary-value problem D0+αy(t)-pD0+βg(t,y(σ(t)))+f(t,y(τ(t)))=0, 0<t<1; y(0)=0, ηy(σ(1))=y(1), where Dα is the standard Riemann-Liouville fractional derivative of order 1<α<2, 0<η<1, p≤0, 0<β<1, β+1-α≥0 the function g is defined as g(t,u):[0,1]×[0,∞)→[0,∞), and g(0,0)=0 the function f is defined as f(t,u):[0,1]×[0,∞)→[0,∞)σ(t), τ(t) are continuous on t and 0≤σ(t), τ(t)≤t. …”
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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

“…We are concerned with the existence and uniqueness of a positive and nondecreasing solution for the following nonlinear fractional m-point boundary value problem: D0+αu(t)+f(t,u(t))=0,  0<t<1,  2<α≤3,  u(0)=u'(0)=0,  u'(1)=∑i=1m-2aiu'(ξi), where D0+α denotes the standard Riemann-Liouville fractional derivative, f:[0,1]×[0,∞)→[0,∞) is a continuous function, ai≥0 for i=1,2,…,m-2, and 0<ξ1<ξ2<⋯<ξm-2<1. …”
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A Novel Approach to Calculation of Reproducing Kernel on Infinite Interval and Applications to Boundary Value Problems by Jing Niu, Yingzhen Lin, Minggen Cui

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Nonlocal boundary value problem in terms of flow for Sturm-Liouville operator in differential and difference statements by Dovlet M. Dovletov

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Existence and Nonexistence of Positive Solutions for a Higher-Order Three-Point Boundary Value Problem by Yongping Sun, Qian Sun, Xiaoping Zhang

“…This paper is concerned with the existence and nonexistence of positive solutions for a nonlinear higher-order three-point boundary value problem. The existence results are obtained by applying a fixed point theorem of cone expansion and compression of functional type due to Avery, Henderson, and O’Regan.…”
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Successive Iteration and Positive Solutions for Nonlinear m-Point Boundary Value Problems on Time Scales by Yanbin Sang

“…We study the existence of positive solutions for a class of m-point boundary value problems on time scales. Our approach is based on the monotone iterative technique and the cone expansion and compression fixed point theorem of norm type. …”
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Multiple Solutions for Second-Order Sturm–Liouville Boundary Value Problems with Subquadratic Potentials at Zero by Dan Liu, Xuejun Zhang, Mingliang Song

“…We deal with the following Sturm–Liouville boundary value problem: −Ptx′t′+Btxt=λ∇xVt,x,  a.e. t∈0,1x0cos  α−P0x′0sin  α=0x1cos  β−P1x′1sin  β=0 Under the subquadratic condition at zero, we obtain the existence of two nontrivial solutions and infinitely many solutions by means of the linking theorem of Schechter and the symmetric mountain pass theorem of Kajikiya. …”
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Existence Theory for q-Antiperiodic Boundary Value Problems of Sequential q-Fractional Integrodifferential Equations by Ravi P. Agarwal, Bashir Ahmad, Ahmed Alsaedi, Hana Al-Hutami

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An Efficient Collocation Method for a Class of Boundary Value Problems Arising in Mathematical Physics and Geometry by A. H. Bhrawy, A. S. Alofi, R. A. Van Gorder

“…We present a numerical method for a class of boundary value problems on the unit interval which feature a type of power-law nonlinearity. …”
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Homotopy Perturbation Method to Obtain Positive Solutions of Nonlinear Boundary Value Problems of Fractional Order by Hossein Jafari, Khadijeh Bagherian, Seithuti P. Moshokoa

“…We use the homotopy perturbation method for solving the fractional nonlinear two-point boundary value problem. The obtained results by the homotopy perturbation method are then compared with the Adomian decomposition method. …”
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Existence of Three Positive Solutions for m-Point Discrete Boundary Value Problems with p-Laplacian by Yanping Guo, Wenying Wei, Yuerong Chen

“…Using a new fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem.…”
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Spectral Criteria for Solvability of Boundary Value Problems and Positivity of Solutions of Time-Fractional Differential Equations by Valentin Keyantuo, Carlos Lizama, Mahamadi Warma

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Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point Theory by Jing Chen, X. H. Tang

“…We study the existence and multiplicity of solutions for the following fractional boundary value problem: (𝑑/𝑑𝑡)((1/2)0𝐷𝑡−𝛽(𝑢′(𝑡))+(1/2)𝑡𝐷𝑇−𝛽(𝑢′(𝑡)))+∇𝐹(𝑡,𝑢(𝑡))=0,a.e.𝑡∈[0,𝑇],𝑢(0)=𝑢(𝑇)=0, where 𝐹(𝑡,⋅) are superquadratic, asymptotically quadratic, and subquadratic, respectively. …”
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Boundary Value Problem for Nonlinear Implicit Generalized Hilfer-Type Fractional Differential Equations with Impulses by Abdelkrim Salim, Mouffak Benchohra, Jamal Eddine Lazreg, Gaston N’Guérékata

“…This article deals with some existence, uniqueness, and Ulam-Hyers-Rassias stability results for a class of boundary value problem for nonlinear implicit fractional differential equations with impulses and generalized Hilfer Fractional derivative. …”
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Existence of Solutions for Fractional Integro-Differential Equation with Multipoint Boundary Value Problem in Banach Spaces by Yulin Zhao, Li Huang, Xuebin Wang, Xianyang Zhu

“…By means of the fixed-point theorem in the cone of strict-set-contraction operators, we consider the existence of a nonlinear multi-point boundary value problem of fractional integro-differential equation in a Banach space. …”
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Infinitely Many Solutions for a Generalized Periodic Boundary Value Problem without the Evenness Assumption by Xiaodong Gu, Mingliang Song

“…In this paper, we investigate infinitely many solutions for the generalized periodic boundary value problem −x″−B0tx+B1tx=λ∇xVt,xa.e.t∈0,1,x1=Mx0,x′1=Nx′0 under the potential function Vt,x without the evenness assumption and obtain two new existence results by the multiple critical point theorem. …”
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Global Structure of Positive Solutions for a Singular Fourth-Order Integral Boundary Value Problem by Wenguo Shen, Tao He

“…We consider fourth-order boundary value problems u′′′′(t)=λh(t)f(u(t)),  0<t<1,  u(0)=∫01‍u(s)dα(s),  u′(0)=u(1)=u′(1)=0, where ∫01‍u(s)dα(s) is a Stieltjes integral with α(t) being nondecreasing and α(t) being not a constant on [0,1]; h(t) may be singular at t=0 and t=1, h∈C((0,1),[0,∞)) with h(t)≢0 on any subinterval of (0,1); f∈C([0,∞),[0,∞)) and f(s)>0 for all s>0, and f0=∞,  f∞=0,  f0=lims→0+f(s)/s,  f∞=lims→+∞f(s)/s. …”
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Positive Solutions to Nonlinear Higher-Order Nonlocal Boundary Value Problems for Fractional Differential Equations by Mujeeb Ur Rehman, Rahmat Ali Khan

“…We use the classical tools from functional analysis to obtain sufficient conditions for the existence and uniqueness of positive solutions to the boundary value problems. We also obtain conditions for the nonexistence of positive solutions to the problem. …”
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On the existence of solution of a two-point boundary value problem in a cylindrical floating zone by Shi Yongdong, Du Liangsheng

“…Existence of one solution for a two-point boundary value problem with a positive parameter Q arising in the study of surface-tension-induced flows of a liquid metal or semiconductor is studied. …”
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