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 Qualitative Analysis of Langevin Integro-Fractional Differential Equation under Mittag–Leffler Functions Power Law

2021 ◽  
Vol 5 (4) ◽  
pp. 266
Author(s):  
Mohammed A. Almalahi ◽  
F. Ghanim ◽  
Thongchai Botmart ◽  
Omar Bazighifan ◽  
Sameh Askar
Keyword(s):  
Differential Equation ◽  
Qualitative Analysis ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Different Types ◽  
Fractional Differential ◽  
Stability Results

This research paper intends to investigate some qualitative analysis for a nonlinear Langevin integro-fractional differential equation. We investigate the sufficient conditions for the existence and uniqueness of solutions for the proposed problem using Banach’s and Krasnoselskii’s fixed point theorems. Furthermore, we discuss different types of stability results in the frame of Ulam–Hyers by using a mathematical analysis approach. The obtained results are illustrated by presenting a numerical example.

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 Complex Transforms for Systems of Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Fractional Differential

We provide a complex transform that maps the complex fractional differential equation into a system of fractional differential equations. The homogeneous and nonhomogeneous cases for equivalence equations are discussed and also nonequivalence equations are studied. Moreover, the existence and uniqueness of solutions are established and applications are illustrated.

Periodic Problem for the Generalized Basset Fractional Differential Equation

2015 ◽  
Vol 18 (5) ◽  
Author(s):  
Svatoslav Stanĕk
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Periodic Problem ◽  
Uniqueness Of Solutions ◽  
Fractional Differential

AbstractWe discuss the existence and uniqueness of solutions to the periodic fractional problem u′ = A

scholarly journals Existence and uniqueness of solutions for nonlinear hyperbolic fractional differential equation with integral boundary conditions

2016 ◽  
Vol 5 (1) ◽  
pp. 18
Author(s):  
Brahim Tellab ◽  
Kamel Haouam
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Integral Boundary Conditions ◽  
Uniqueness Of Solutions ◽  
Nonlinear Fractional Differential Equation ◽  
Integral Boundary ◽  
Krasnoselskii Fixed Point Theorem ◽  
Fractional Differential

<p>In this paper, we investigate the existence and uniqueness of solutions for second order nonlinear fractional differential equation with integral boundary conditions. Our result is an application of the Banach contraction principle and the Krasnoselskii fixed point theorem.</p>

scholarly journals Existence and Uniqueness of Solutions for BVP of Nonlinear Fractional Differential Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Cheng-Min Su ◽  
Jian-Ping Sun ◽  
Ya-Hong Zhao
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Banach Contraction Principle ◽  
Uniqueness Of Solutions ◽  
Nonlinear Fractional Differential Equation ◽  
Nonlinear Alternative ◽  
Banach Contraction ◽  
Fractional Differential

In this paper, we study the existence and uniqueness of solutions for the following boundary value problem of nonlinear fractional differential equation: D0+qCut=ft,ut,  t∈0,1, u0=u′′0=0,  D0+σ1Cu1=λI0+σ2u1, where 2<q<3, 0<σ1≤1, σ2>0, and λ≠Γ2+σ2/Γ2-σ1. The main tools used are nonlinear alternative of Leray-Schauder type and Banach contraction principle.

scholarly journals A Study of Impulsive Multiterm Fractional Differential Equations with Single and Multiple Base Points and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-28 ◽  
Author(s):  
Yuji Liu ◽  
Bashir Ahmad
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Logistic Models ◽  
Base Point ◽  
Asymptotic Behavior Of Solutions ◽  
Uniqueness Of Solutions ◽  
Base Points ◽  
Fractional Differential

We discuss the existence and uniqueness of solutions for initial value problems of nonlinear singular multiterm impulsive Caputo type fractional differential equations on the half line. Our study includes the cases for a single base point fractional differential equation as well as multiple base points fractional differential equation. The asymptotic behavior of solutions for the problems is also investigated. We demonstrate the utility of our work by applying the main results to fractional-order logistic models.

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