On Solutions to Fractional Iterative Differential Equations with Caputo Derivative by Alemnew Abera, Benyam Mebrate

“…First, the existence and uniqueness of the iterative fractional differential equation cDαcxt=ft,xt,xgxt are presented using the fixed-point theorem by imposing some conditions on f and g. …”
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Existence and Nonexistence of Positive Solutions for Fractional Three-Point Boundary Value Problems with a Parameter by Yunhong Li, Weihua Jiang

“…In this work, we investigate the existence and nonexistence of positive solutions for p-Laplacian fractional differential equation with a parameter. On the basis of the properties of Green’s function and Guo-Krasnosel’skii fixed point theorem on cones, the existence and nonexistence of positive solutions are obtained for the boundary value problems. …”
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The Periodic Solutions of the Compound Singular Fractional Differential System with Delay by XuTing Wei, XuanZhu Lu

“…Especially, for two-dimensional compound singular fractional differential equation with delay, the criteria of existence of periodic solution are obtained. …”
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Positive Solutions of a Fractional Boundary Value Problem with Changing Sign Nonlinearity by Yongqing Wang, Lishan Liu, Yonghong Wu

“…We discuss the existence of positive solutions of a boundary value problem of nonlinear fractional differential equation with changing sign nonlinearity. …”
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Existence Results of Langevin Equations with Caputo–Hadamard Fractional Operator by Sombir Dhaniya, Anoop Kumar, Aziz Khan, Thabet Abdeljawad, Manar A. Alqudah

“…In this manuscript, we deal with a nonlinear Langevin fractional differential equation that involves the Caputo–Hadamard and Caputo fractional operators, with nonperiodic and nonlocal integral boundary conditions. …”
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Fixed Points for Multivalued Suzuki Type (θ,R)-Contraction Mapping with Applications by Mujahid Abbas, Hira Iqbal, Adrian Petrusel

“…As an application of our results, we obtain a homotopy result, proving the existence of a solution for a second-order differential equation and for a first-order fractional differential equation.…”
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Solutions of Conformable Fractional-Order SIR Epidemic Model by Atimad Harir, Said Malliani, Lalla Saadia Chandli

“…These models are nonlinear system of conformable fractional differential equation (CFDE) that has no analytic solution. …”
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Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value Problem by Wen Lian, Zhanbing Bai

“…The existence and multiplicity of positive solutions for the nonlinear fractional differential equation boundary value problem (BVP) DC0+αyx+fx,yx=0,   0<x<1, y0=y′1=y″0=0 is established, where 2<α≤3,  CD0+α is the Caputo fractional derivative, and f:0,1×0,∞⟶0,∞ is a continuous function. …”
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Analysis of Fractional Kundu-Eckhaus and Massive Thirring Equations Using a Hybridization Scheme by Muhammad Nadeem, Hanan A. Wahash

“…To avoid some assumptions and hypothesis, we apply a two-scale approach for such a nonlinear complex model. The fractional differential equation may be transformed into its partner equation using He’s fractional complex transform, and then, the nonlinear elements can be readily handled using the homotopy perturbation method (HPM). …”
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Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations by Khaled A. Gepreel, Taher A. Nofal, Fawziah M. Alotaibi

“…Also, we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations. …”
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Positive Solutions for a Coupled System of Nonlinear Semipositone Fractional Boundary Value Problems by S. Nageswara Rao, M. Zico Meetei

“…In this paper, we consider a four-point coupled boundary value problem for system of the nonlinear semipositone fractional differential equation D0+αu(t)+λf(t,u(t),v(t))=0,  0<t<1, D0+αv(t)+μg(t,u(t),v(t))=0,  0<t<1, u(0)=v(0)=0,  a1D0+βu(1)=b1D0+βv(ξ), a2D0+βv(1)=b2D0+βu(η),  η,ξ∈(0,1), where the coefficients ai,bi,i=1,2 are real positive constants, α∈(1,2],β∈(0,1],D0+α, D0+β are the standard Riemann-Liouville derivatives. …”
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Numerical Vibration Displacement Solutions of Fractional Drawing Self-Excited Vibration Model Based on Fractional Legendre Functions by Jiaquan Xie, Yongjiang Zheng, Zhongkai Ren, Tao Wang, Guangxian Shen

“…In practice, due to the fact that the phenomenon of drawing self-excited vibration can be deemed as one of the hunting phenomena of the mechanical system, this study focuses on investigating the drawing self-excited vibration process through proposing the fractional differential equation model of hunting phenomenon of the mechanical system. …”
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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

“…The existence, uniqueness, and asymptotic behavior of positive solutions to the singular nonlocal integral boundary value problem for fractional differential equation are obtained. Our analysis relies on Schauder's fixed-point theorem and upper and lower solution method.…”
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An innovative analytical method utilizing aboodh residual power series for solving the time-fractional newell-whitehead-segel equation by Seyed Edalatpanah, Eisa Abdolmaleki

“…One of the key advantages of our approach is that the Aboodh transformation operator converts the fractional differential equation into an algebraic equation, thereby significantly reducing the computational effort required in the subsequent algebraic steps. …”
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On the Possibility of the Jerk Derivative in Electrical Circuits by J. F. Gómez-Aguilar, J. Rosales-García, R. F. Escobar-Jiménez, M. G. López-López, V. M. Alvarado-Martínez, V. H. Olivares-Peregrino

“…The LC circuit has a frequency ω dependent on the order of the fractional differential equation γ, since it is defined as ω(γ)=ω0γγ1-γ, where ω0 is the fundamental frequency. …”
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Analysis of Caputo Impulsive Fractional Order Differential Equations with Applications by Lakshman Mahto, Syed Abbas, Angelo Favini

“…We also discuss Caputo impulsive fractional differential equations with finite delay. The results proven are new and compliment the existing one.…”
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Novel Analysis of Fuzzy Fractional Emden-Fowler Equations within New Iterative Transform Method by M. Mossa Al-Sawalha, Naila Amir, Rasool Shah, Muhammad Yar

“…The analytical behavior of fractional differential equations is often puzzling and difficult to predict under uncertainty. …”
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The Yang-Laplace Transform for Solving the IVPs with Local Fractional Derivative by Chun-Guang Zhao, Ai-Min Yang, Hossein Jafari, Ahmad Haghbin

“…Analytical solutions for the homogeneous and nonhomogeneous local fractional differential equations are discussed by using the Yang-Laplace transform.…”
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Uniqueness and Existence of Solution for a System of Fractional q-Difference Equations by Wen-Xue Zhou, Hai-zhong Liu

“…We prove the existence and uniqueness of solution for a system of fractional differential equations. Our results are based on the nonlinear alternative of Leray-Schauder type and Banach’s fixed-point theorem.…”
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Analytical Techniques for Studying Fractional-Order Jaulent–Miodek System Within Algebraic Context by Yousuf Alkhezi, Ahmad Shafee

“…The proposed study seeks to investigate various analytical and numerical techniques for solving fractional differential equations, with a particular focus on their applications in mathematical modeling and scientific research within the field of algebra. …”
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