scholarly journals A study on fractional differential equations using the fractional Fourier transform

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Porpattama Hammachukiattikul ◽  
Arusamy Mohanapriya ◽  
Anumanthappa Ganesh ◽  
Grienggrai Rajchakit ◽  
Vediyappan Govindan ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Existence And Uniqueness ◽  
Order Differential Equation ◽  
Fractional Fourier Transform ◽  
Nonlinear Problems ◽  
Ulam Stability ◽  
Fractional Order Differential Equation ◽  
Fractional Differential ◽  
Stability Results ◽  
Rassias Stability

AbstractThis study aims to use the fractional Fourier transform for analyzing various types of Hyers–Ulam stability pertaining to the linear fractional order differential equation with Atangana and Baleanu fractional derivative. Specifically, we establish the Hyers–Ulam–Rassias stability results and examine their existence and uniqueness for solving nonlinear problems. Simulation examples are presented to validate the results.

scholarly journals Fractional Fourier transform and stability of fractional differential equation on Lizorkin space

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Bundit Unyong ◽  
Arusamy Mohanapriya ◽  
Anumanthappa Ganesh ◽  
Grienggrai Rajchakit ◽  
Vediyappan Govindan ◽  
...  
Keyword(s):  
Differential Equation ◽  
Fourier Transform ◽  
Fractional Differential Equation ◽  
Fractional Fourier Transform ◽  
Nonlinear Problems ◽  
Uniqueness Of Solutions ◽  
Lizorkin Space ◽  
Fractional Differential ◽  
Delay Differential ◽  
Stability Results

Abstract In the current study, we conduct an investigation into the Hyers–Ulam stability of linear fractional differential equation using the Riemann–Liouville derivatives based on fractional Fourier transform. In addition, some new results on stability conditions with respect to delay differential equation of fractional order are obtained. We establish the Hyers–Ulam–Rassias stability results as well as examine their existence and uniqueness of solutions pertaining to nonlinear problems. We provide examples that indicate the usefulness of the results presented.

scholarly journals Existence and Ulam stability for implicit fractional q-difference equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Nadjet Laledj ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Ulam Stability ◽  
Uniqueness Of Solutions ◽  
Stability Results ◽  
Rassias Stability

AbstractThis paper deals with some existence, uniqueness and Ulam–Hyers–Rassias stability results for a class of implicit fractional q-difference equations. Some applications are made of some fixed point theorems in Banach spaces for the existence and uniqueness of solutions, next we prove that our problem is generalized Ulam–Hyers–Rassias stable. Two illustrative examples are given in the last section.

Existence, Uniqueness and Stability of Implicit Switched Coupled Fractional Differential Equations of ψ$\boldsymbol{\psi}$-Hilfer Type

2020 ◽  
Vol 21 (3-4) ◽  
pp. 327-337 ◽  
Author(s):  
Manzoor Ahmad ◽  
Akbar Zada ◽  
Xiaoming Wang
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Ulam Stability ◽  
Uniqueness Of Solutions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential System ◽  
Fractional Differential ◽  
Fixed Point Techniques ◽  
Rassias Stability

AbstractIn this article, we study the existence and uniqueness of solutions of a switched coupled implicit ψ-Hilfer fractional differential system. The existence and uniqueness results are obtained by using fixed point techniques. Further, we investigate different kinds of stability such as Hyers–Ulam stability and Hyers–Ulam–Rassias stability. Finally, an example is provided to illustrate the obtained results.

scholarly journals Existence, uniqueness, approximation of solutions and Ealpha-Ulam stability results for a class of nonlinear fractional differential equations involving psi-Caputo derivative with initial conditions

2021 ◽  
Vol 25 (1) ◽  
pp. 1-30
Author(s):  
Choukri Derbazi ◽  
Zidane Baitiche ◽  
Mouffak Benchohra ◽  
Gaston N'guérékata
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Initial Conditions ◽  
Ulam Stability ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
Stability Results

The main purpose of this paper is to study the existence, uniqueness, Ea-Ulam stability results, and other properties of solutions for certain classes of nonlinear fractional differential equations involving the ps-Caputo derivative with initial conditions. Modern tools of functional analysis are applied to obtain the main results. More precisely using Weissinger's fixed point theorem and Schaefer's fixed point theorem the existence and uniqueness results of solutions are proven in the bounded domain. While the well known Banach fixed point theorem coupled with Bielecki type norm are used with the end goal to establish sufficient conditions for existence and uniqueness results on unbounded domains. Meanwhile, the monotone iterative technique combined with the method of upper and lower solutions is used to prove the existence and uniqueness of extremal solutions. Furthermore, by means of new generalizations of Gronwall's inequality, different kinds of Ea-Ulam stability of the proposed problem are studied. Finally, as applications of the theoretical results, some examples are given to illustrate the feasibility and correctness of the main results.

scholarly journals A Fixed-Point Approach to the Hyers–Ulam Stability of Caputo–Fabrizio Fractional Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 647 ◽  
Author(s):  
Kui Liu ◽  
Michal Fečkan ◽  
JinRong Wang
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Compact Interval ◽  
Ulam Stability ◽  
Fixed Point Approach ◽  
Fractional Differential ◽  
Stability Results ◽  
Rassias Stability

In this paper, we study Hyers–Ulam and Hyers–Ulam–Rassias stability of nonlinear Caputo–Fabrizio fractional differential equations on a noncompact interval. We extend the corresponding uniqueness and stability results on a compact interval. Two examples are given to illustrate our main results.

scholarly journals Existence and uniqueness results for a class of fractional differential equations with an integral fractional boundary condition

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1241-1249 ◽  
Author(s):  
Asghar Ahmadkhanlu
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Order Differential Equation ◽  
Necessary Conditions ◽  
Boundary Value ◽  
Fractional Order Differential Equation ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Sufficient And Necessary Conditions ◽  
Fractional Differential

The aim of this work is to study a class of boundary value problem including a fractional order differential equation. Sufficient and necessary conditions will be presented for the existence and uniqueness of solution of this fractional boundary value problem.

scholarly journals Impulsive Coupled System of Fractional Differential Equations with Caputo–Katugampola Fuzzy Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Leila Sajedi ◽  
Nasrin Eghbali ◽  
Hassen Aydi
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Stability Of Solutions ◽  
Fractional Differential ◽  
The Given ◽  
Stability Results ◽  
Rassias Stability

In this article, we investigate the existence, uniqueness, and different kinds of Ulam–Hyers stability of solutions of an impulsive coupled system of fractional differential equations by using the Caputo–Katugampola fuzzy fractional derivative. We applied the Perov-type fixed point theorem to prove the existence and uniqueness of the proposed system. Furthermore, the Ulam–Hyers–Rassias stability and Ulam–Hyers–Rassias–Mittag-Leffler’s stability results for the given system are discussed.

scholarly journals Existence and Stability Results for a Fractional Order Differential Equation with Non-Conjugate Riemann-Stieltjes Integro-Multipoint Boundary Conditions

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 249 ◽  
Author(s):  
Bashir Ahmad ◽  
Ymnah Alruwaily ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Boundary Conditions ◽  
Fractional Order ◽  
Order Differential Equation ◽  
Fractional Order Differential Equation ◽  
Uniqueness Of Solutions ◽  
Multipoint Boundary ◽  
Existence And Stability ◽  
Multipoint Boundary Conditions ◽  
Stability Results ◽  
Rassias Stability

We discuss the existence and uniqueness of solutions for a Caputo-type fractional order boundary value problem equipped with non-conjugate Riemann-Stieltjes integro-multipoint boundary conditions on an arbitrary domain. Modern tools of functional analysis are applied to obtain the main results. Examples are constructed for the illustration of the derived results. We also investigate different kinds of Ulam stability, such as Ulam-Hyers stability, generalized Ulam-Hyers stability, and Ulam-Hyers-Rassias stability for the problem at hand.

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