Existence and uniqueness results for a nonlinear singular fractional differential equation of order $ \sigma\in(1, 2) $

Bilgici, S.S.; Şan, Müfit

doi:10.3934/math.2021754

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…For further related results, we refer the reader to [12][13][14][15][16][17][18][19][20][21] and the references therein. Motivated by the approach used in [11], we consider the problem:…”

Section: Introductionmentioning

confidence: 99%

Existence and Global Asymptotic Behavior of Positive Solutions for Superlinear Singular Fractional Boundary Value Problems

Aljarallah

Bachar

2023

Fractal Fract

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In this paper, we provide sufficient conditions for the existence, uniqueness and global behavior of a positive continuous solution to some nonlinear Riemann-Liouville fractional boundary value problems. The nonlinearity is allowed to be singular at the boundary. The proofs are based on perturbation techniques after reducing the considered problem to the equivalent Fredholm integral equation of the second kind. Some examples are given to illustrate our main results.

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“…For further related results, we refer the reader to [12][13][14][15][16][17][18][19][20][21] and the references therein. Motivated by the approach used in [11], we consider the problem:…”

Section: Introductionmentioning

confidence: 99%

Existence and Global Asymptotic Behavior of Positive Solutions for Superlinear Singular Fractional Boundary Value Problems

Aljarallah

Bachar

2023

Fractal Fract

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On the Existence and Stability of Solutions for a Class of Fractional Riemann–Liouville Initial Value Problems

Castro

Silva

2023

Mathematics

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This article deals with a class of nonlinear fractional differential equations, with initial conditions, involving the Riemann–Liouville fractional derivative of order α∈(1,2). The main objectives are to obtain conditions for the existence and uniqueness of solutions (within appropriate spaces), and to analyze the stabilities of Ulam–Hyers and Ulam–Hyers–Rassias types. In fact, different conditions for the existence and uniqueness of solutions are obtained based on the analysis of an associated class of fractional integral equations and distinct fixed-point arguments. Additionally, using a Bielecki-type metric and some additional contractive arguments, conditions are also obtained to guarantee Ulam–Hyers and Ulam–Hyers–Rassias stabilities for the problems under analysis. Examples are also included to illustrate the theory.

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A study for a higher order Riemann-Liouville fractional differential equation with weakly singularity

San,

Ramazan

2024

era

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<abstract><p>In this paper, we study an initial value problem with a weakly singular nonlinear fractional differential equation of higher order. First, we establish the existence of global solutions to the problem within the appropriate function space. We then introduce a generalized Riemann-Liouville mean value theorem. Using this theorem, we prove the Nagumo-type uniqueness theorem for the stated problem. Moreover, we give two examples to illustrate the applicability of the existence and uniqueness theorems.</p></abstract>

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Existence and uniqueness results for a nonlinear singular fractional differential equation of order $ \sigma\in(1, 2) $

Cited by 3 publications

References 13 publications

Existence and Global Asymptotic Behavior of Positive Solutions for Superlinear Singular Fractional Boundary Value Problems

Existence and Global Asymptotic Behavior of Positive Solutions for Superlinear Singular Fractional Boundary Value Problems

On the Existence and Stability of Solutions for a Class of Fractional Riemann–Liouville Initial Value Problems

A study for a higher order Riemann-Liouville fractional differential equation with weakly singularity

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