Comment for “Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel”

Abstract In this manuscript, we examine the existence and the Ulam stability of solutions for a class of boundary value problems for nonlinear implicit fractional differential equations with instantaneous impulses in Banach spaces. The results are based on fixed point theorems of Darbo and Mönch associated with the technique of measure of noncompactness. We provide some examples to indicate the applicability of our results.

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Existence and Uniqueness on Solutions for Anti-Periodic Boundary Value Problems of Singular Fractional Differential Equations with P-Laplacian Operator

Advances in Applied Mathematics ◽

10.12677/aam.2021.1011386 ◽

2021 ◽

Vol 10 (11) ◽

pp. 3650-3658

Author(s):

婷婷张

Keyword(s):

Differential Equations ◽

Boundary Value Problems ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Periodic Boundary ◽

Boundary Value ◽

Laplacian Operator ◽

Periodic Boundary Value Problems ◽

Singular Fractional Differential Equations ◽

Fractional Differential

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GLOBAL EXISTENCE OF SOLUTIONS FOR A SYSTEM OF SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECTS

Journal of applied mathematics & informatics ◽

10.14317/jami.2015.327 ◽

2015 ◽

Vol 33 (3_4) ◽

pp. 327-342 ◽

Cited By ~ 8

Author(s):

YUJI LIU ◽

PATRICIA J.Y. WONG

Keyword(s):

Global Existence ◽

Differential Equations ◽

Fractional Differential Equations ◽

Existence Of Solutions ◽

Global Existence Of Solutions ◽

Singular Fractional Differential Equations ◽

Fractional Differential

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Some new uniqueness and Ulam stability results for a class of Multi-Terms fractional differential equations in the framework of Generalized Caputo Fractional Derivative using the Φ\Phi-fractional Bielecki-type norm

TURKISH JOURNAL OF MATHEMATICS ◽

10.3906/mat-2011-92 ◽

2021 ◽

Keyword(s):

Differential Equations ◽

Fractional Derivative ◽

Fractional Differential Equations ◽

Caputo Fractional Derivative ◽

Ulam Stability ◽

Fractional Differential ◽

Stability Results

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Hyers‐Ulam stability analysis to implicit Cauchy problem of fractional differential equations with impulsive conditions

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.5292 ◽

2018 ◽

Vol 41 (17) ◽

pp. 8329-8343 ◽

Cited By ~ 22

Author(s):

Kamal Shah ◽

Arshad Ali ◽

Samia Bushnaq

Keyword(s):

Cauchy Problem ◽

Stability Analysis ◽

Differential Equations ◽

Fractional Differential Equations ◽

Ulam Stability ◽

Impulsive Conditions ◽

Fractional Differential

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Investigating a Class of Nonlinear Fractional Differential Equations and Its Hyers-Ulam Stability by Means of Topological Degree Theory

Numerical Functional Analysis and Optimization ◽

10.1080/01630563.2019.1604545 ◽

2019 ◽

Vol 40 (12) ◽

pp. 1355-1372 ◽

Cited By ~ 8

Author(s):

Kamal Shah ◽

Wajid Hussain

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Topological Degree ◽

Degree Theory ◽

Ulam Stability ◽

Topological Degree Theory ◽

Nonlinear Fractional Differential Equations ◽

Fractional Differential

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Hyers–Ulam stability of a coupled system of fractional differential equations of Hilfer–Hadamard type

Demonstratio Mathematica ◽

10.1515/dema-2019-0024 ◽

2019 ◽

Vol 52 (1) ◽

pp. 283-295 ◽

Cited By ~ 14

Author(s):

Manzoor Ahmad ◽

Akbar Zada ◽

Jehad Alzabut

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Differential Equations ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Coupled System ◽

Ulam Stability ◽

Fractional Differential System ◽

Different Types ◽

Fractional Differential

AbstractIn this paper, existence and uniqueness of solution for a coupled impulsive Hilfer–Hadamard type fractional differential system are obtained by using Kransnoselskii’s fixed point theorem. Different types of Hyers–Ulam stability are also discussed.We provide an example demonstrating consistency to the theoretical findings.

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