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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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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Forced-Perturbed Fractional Differential Equations of Higher Order: Asymptotic Properties of Non-Oscillatory Solutions by Said R. Grace, Gokula N. Chhatria, S. Kaleeswari, Yousef Alnafisah, Osama Moaaz

“…This study investigates the asymptotic behavior of non-oscillatory solutions to forced-perturbed fractional differential equations with the Caputo fractional derivative. …”
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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 study existence of positive solutions to nonlinear higher-order nonlocal boundary value problems corresponding to fractional differential equation of the type 𝑐𝒟𝛿0+𝑢(𝑡)+𝑓(𝑡,𝑢(𝑡))=0, 𝑡∈(0,1), 0<𝑡<1. 𝑢(1)=𝛽𝑢(𝜂)+𝜆2, 𝑢(0)=𝛼𝑢(𝜂)−𝜆1, 𝑢(0)=0, 𝑢(0)=0⋯𝑢(𝑛−1)(0)=0, where, 𝑛−1<𝛿<𝑛, 𝑛(≥3)∈ℕ, 0<𝜂,𝛼,𝛽<1, the boundary parameters 𝜆1,𝜆2∈ℝ+ and 𝑐𝐷𝛿0+ is the Caputo fractional derivative. …”
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A Time-Space Collocation Spectral Approximation for a Class of Time Fractional Differential Equations by Fenghui Huang

“…A numerical scheme is presented for a class of time fractional differential equations with Dirichlet's and Neumann's boundary conditions. …”
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Existence of Positive Solutions for m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation by Moustafa El-Shahed, Wafa M. Shammakh

“…We investigate an m-point boundary value problem for nonlinear fractional differential equations. The associated Green function for the boundary value problem is given at first, and some useful properties of the Green function are obtained. …”
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Existence and Uniqueness Results for Fractional Differential Equations with Riemann-Liouville Fractional Integral Boundary Conditions by Mohamed I. Abbas

“…We prove the existence and uniqueness of solution for fractional differential equations with Riemann-Liouville fractional integral boundary conditions. …”
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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

“…Finally, we provide an application to fractional differential equations to show the validity of the main result.…”
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Positive Solutions for Three-Point Boundary Value Problem of Fractional Differential Equation with -Laplacian Operator by Shang-lin Yao, Guo-hui Wang, Zhi-ping Li, Li-jun Yu

“…We investigate the existence of multiple positive solutions for three-point boundary value problem of fractional differential equation with -Laplacian operator , where are the standard Riemann-Liouville derivatives with , and the constant is a positive number satisfying ; -Laplacian operator is defined as . …”
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The Eigenvalue Problem for Caputo Type Fractional Differential Equation with Riemann-Stieltjes Integral Boundary Conditions by Wenjie Ma, Yujun Cui

“…In this paper, we investigate the eigenvalue problem for Caputo fractional differential equation with Riemann-Stieltjes integral boundary conditions Dc0+θp(y)+μf(t,p(y))=0, y∈[0,1], p(0)=p′′(0)=0, p(1)=∫01p(y)dA(y), where Dc0+θ is Caputo fractional derivative, θ∈(2,3], and f:[0,1]×[0,+∞)→[0,+∞) is continuous. …”
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The Existence of Solutions for Four-Point Coupled Boundary Value Problems of Fractional Differential Equations at Resonance by Yumei Zou, Lishan Liu, Yujun Cui

“…A four-point coupled boundary value problem of fractional differential equations is studied. Based on Mawhin’s coincidence degree theory, some existence theorems are obtained in the case of resonance.…”
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Remark on Existence and Uniqueness of Solutions for a Coupled System of Multiterm Nonlinear Fractional Differential Equations by Huichao Zou, Yonghong Fan

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Existence and Uniqueness for a System of Caputo-Hadamard Fractional Differential Equations with Multipoint Boundary Conditions by S. Nageswara Rao, Ahmed Hussein Msmali, Manoj Singh, Abdullah Ali H. Ahmadini

“…In this paper, we study existence and uniqueness of solutions for a system of Caputo-Hadamard fractional differential equations supplemented with multi-point boundary conditions. …”
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Existence and Ulam–Hyers stability results for Caputo–Hadamard fractional differential equations with non-instantaneous impulses by Mesfin Teshome Beyene, Mitiku Daba Firdi, Tamirat Temesgen Dufera

“…Abstract In this manuscript, we investigated the existence, uniqueness, and Ulam–Hyers stability results of solutions to implicit Caputo–Hadamard fractional differential equations with noninstantaneous impulses and δ − d e r i v a t i v e $\delta -derivative$ initial conditions. …”
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A Contraction Fixed Point Theorem in Partially Ordered Metric Spaces and Application to Fractional Differential Equations by Xiangbing Zhou, Wenquan Wu, Hongjiang Ma

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Higher-order fuzzy fractional differential equations: on the existence, uniqueness and Hyers–Ulam–Rassias stability of solutions by Brahim Ghrissi, Abdelkader Amara, Youcef Henka

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Existence and Uniqueness Results for a Coupled System of Nonlinear Fractional Differential Equations with Antiperiodic Boundary Conditions by Huina Zhang, Wenjie Gao

“…This paper studies the existence and uniqueness of solutions for a coupled system of nonlinear fractional differential equations of order α,β∈(4,5] with antiperiodic boundary conditions. …”
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Positive Solutions for a Weakly Singular Hadamard-Type Fractional Differential Equation with Changing-Sign Nonlinearity by Xinguang Zhang, Lixin Yu, Jiqiang Jiang, Yonghong Wu, Yujun Cui

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Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations by Qingxue Huang, Fuqiang Zhao, Jiaquan Xie, Lifeng Ma, Jianmei Wang, Yugui Li

“…In this paper, a robust, effective, and accurate numerical approach is proposed to obtain the numerical solution of fractional differential equations. The principal characteristic of the approach is the new orthogonal functions based on shifted Legendre polynomials to the fractional calculus. …”
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Monotone and Concave Positive Solutions to a Boundary Value Problem for Higher-Order Fractional Differential Equation by Jinhua Wang, Hongjun Xiang, Yuling Zhao

“…We consider boundary value problem for nonlinear fractional differential equation D0+αu(t)+f(t,u(t))=0,  0<t<1,  n-1<α≤n,  n>3,  u(0)=u'(1)=u′′(0)=⋯=u(n-1)(0)=0, where D0+α denotes the Caputo fractional derivative. …”
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