New Sufficient Conditions to Ulam Stabilities for a Class of Higher Order Integro-Differential Equations

In this work, we present sufficient conditions in order to establish different types of Ulam stabilities for a class of higher order integro-differential equations. In particular, we consider a new kind of stability, the σ-semi-Hyers-Ulam stability, which is in some sense between the Hyers–Ulam and the Hyers–Ulam–Rassias stabilities. These new sufficient conditions result from the application of the Banach Fixed Point Theorem, and by applying a specific generalization of the Bielecki metric.

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Uniqueness and Stability Results on Non-local Stochastic Random Impulsive Integro-Differential Equations

Journal of Mathematical Analysis and Modeling ◽

10.48185/jmam.v2i3.346 ◽

2021 ◽

Vol 2 (3) ◽

pp. 9-20

Author(s):

VARSHINI S ◽

BANUPRIYA K ◽

RAMKUMAR K ◽

RAVIKUMAR K

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Differential Equations ◽

Point Theorem ◽

Sufficient Conditions ◽

Banach Fixed Point Theorem ◽

Local Conditions ◽

Non Local ◽

Inequality Techniques ◽

Stability Results

The paper is concerned with stochastic random impulsive integro-differential equations with non-local conditions. The sufficient conditions guarantees uniqueness of mild solution derived using Banach fixed point theorem. Stability of the solution is derived by incorporating Banach fixed point theorem with certain inequality techniques.

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Existence of nonoscillatory solutions of higher order neutral differential equations

Filomat ◽

10.2298/fil1608147c ◽

2016 ◽

Vol 30 (8) ◽

pp. 2147-2153 ◽

Cited By ~ 1

Author(s):

T. Candan

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Differential Equations ◽

Point Theorem ◽

Sufficient Conditions ◽

Higher Order ◽

Nonoscillatory Solutions ◽

Deviating Arguments ◽

Neutral Differential Equations ◽

Distributed Deviating Arguments

This article is concerned with nonoscillatory solutions of higher order nonlinear neutral differential equations with deviating and distributed deviating arguments. By using Knaster-Tarski fixed point theorem, new sufficient conditions are established. Illustrative example is given to show applicability of results.

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Hyers–Ulam Stability and Existence of Solutions for Differential Equations with Caputo–Fabrizio Fractional Derivative

Mathematics ◽

10.3390/math7040333 ◽

2019 ◽

Vol 7 (4) ◽

pp. 333 ◽

Cited By ~ 11

Author(s):

Kui Liu ◽

Michal Fečkan ◽

D. O’Regan ◽

JinRong Wang

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Differential Equations ◽

Point Theorem ◽

Stability Result ◽

Banach Fixed Point Theorem ◽

Ulam Stability ◽

Uniqueness Of Solutions ◽

Transform Method ◽

Fractional Differential

In this paper, the Hyers–Ulam stability of linear Caputo–Fabrizio fractional differential equation is established using the Laplace transform method. We also derive a generalized Hyers–Ulam stability result via the Gronwall inequality. In addition, we establish existence and uniqueness of solutions for nonlinear Caputo–Fabrizio fractional differential equations using the generalized Banach fixed point theorem and Schaefer’s fixed point theorem. Finally, two examples are given to illustrate our main results.

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Ulam Type Stability for a Coupled System of Boundary Value Problems of Nonlinear Fractional Differential Equations

Journal of Function Spaces ◽

10.1155/2017/3046013 ◽

2017 ◽

Vol 2017 ◽

pp. 1-8 ◽

Cited By ~ 10

Author(s):

Aziz Khan ◽

Kamal Shah ◽

Yongjin Li ◽

Tahir Saeed Khan

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Differential Equations ◽

Point Theorem ◽

Sufficient Conditions ◽

Coupled System ◽

Generalized Metric Space ◽

Ulam Stability ◽

Fractional Differential ◽

Necessary And Sufficient

We discuss existence, uniqueness, and Hyers-Ulam stability of solutions for coupled nonlinear fractional order differential equations (FODEs) with boundary conditions. Using generalized metric space, we obtain some relaxed conditions for uniqueness of positive solutions for the mentioned problem by using Perov’s fixed point theorem. Moreover, necessary and sufficient conditions are obtained for existence of at least one solution by Leray-Schauder-type fixed point theorem. Further, we also develop some conditions for Hyers-Ulam stability. To demonstrate our main result, we provide a proper example.

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Oscillation results for higher order nonlinear neutral differential equations with positive and negative coefficients

Journal of Applied Analysis ◽

10.1515/jaa-2015-0011 ◽

2015 ◽

Vol 21 (2) ◽

Cited By ~ 1

Author(s):

Saroj Panigrahi ◽

Rakhee Basu

Keyword(s):

Fixed Point ◽

Asymptotic Behavior ◽

Fixed Point Theorem ◽

Differential Equations ◽

Sufficient Conditions ◽

Higher Order ◽

Asymptotic Behavior Of Solutions ◽

Banach Fixed Point Theorem ◽

Neutral Differential Equations ◽

Positive And Negative Coefficients

AbstractIn this paper, the authors investigated oscillatory and asymptotic behavior of solutions of a class of nonlinear higher order neutral differential equations with positive and negative coefficients. The results in this paper generalize the results of Tripathy, Panigrahi and Basu [Fasc. Math. 52 (2014), 155–174]. We establish new conditions which guarantees that every solution either oscillatory or converges to zero. Moreover, using the Banach Fixed Point Theorem sufficient conditions are obtained for the existence of bounded positive solutions. Examples are considered to illustrate the main results.

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On the behavior of solutions of fractional differential equations on time scale via Hilfer fractional derivatives

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2018-0060 ◽

2018 ◽

Vol 21 (4) ◽

pp. 1120-1138 ◽

Cited By ~ 1

Author(s):

Devaraj Vivek ◽

Kuppusamy Kanagarajan ◽

Seenith Sivasundaram

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Differential Equations ◽

Point Theorem ◽

Fractional Differential Equations ◽

Sufficient Conditions ◽

Banach Fixed Point Theorem ◽

Uniqueness Of Solutions ◽

Existence And Stability ◽

Fractional Differential

Abstract In this paper, we study the existence and stability of Hilfer-type fractional differential equations (dynamic equations) on time scales. We obtain sufficient conditions for existence and uniqueness of solutions by using classical fixed point theorems such as Schauder's fixed point theorem and Banach fixed point theorem. In addition, Ulam stability of the proposed problem is also discussed. As in application, we provide an example to illustrate our main results.

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Existence results of ψ-Hilfer integro-differential equations with fractional order in Banach space

Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica ◽

10.2478/aupcsm-2020-0013 ◽

2020 ◽

Vol 19 (1) ◽

pp. 171-192

Author(s):

Mohammed A. Almalahi ◽

Satish K. Panchal

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Differential Equations ◽

Point Theorem ◽

Fixed Point Theory ◽

Point Theory ◽

Banach Fixed Point Theorem ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Mönch Fixed Point Theorem

AbstractIn this article we present the existence and uniqueness results for fractional integro-differential equations with ψ-Hilfer fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Mönch fixed point theorem and the Banach fixed point theorem. Furthermore, we discuss Eα -Ulam-Hyers stability of the presented problem. Also, we use the generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of the δ-approximate solution.

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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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The Existence and Uniqueness of Solutions for a Class of Nonlinear Fractional Differential Equations with Infinite Delay

Abstract and Applied Analysis ◽

10.1155/2013/592964 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8 ◽

Cited By ~ 3

Author(s):

Azizollah Babakhani ◽

Dumitru Baleanu ◽

Ravi P. Agarwal

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Differential Equations ◽

Point Theorem ◽

Existence And Uniqueness ◽

Fractional Derivatives ◽

Infinite Delay ◽

Banach Fixed Point Theorem ◽

Uniqueness Of Solutions ◽

Fractional Differential

We prove the existence and uniqueness of solutions for two classes of infinite delay nonlinear fractional order differential equations involving Riemann-Liouville fractional derivatives. The analysis is based on the alternative of the Leray-Schauder fixed-point theorem, the Banach fixed-point theorem, and the Arzela-Ascoli theorem inΩ={y:(−∞,b]→ℝ:y|(−∞,0]∈ℬ}such thaty|[0,b]is continuous andℬis a phase space.

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