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 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.

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 ON THE NONLINEAR IMPULSIVE Ψ–HILFER FRACTIONAL DIFFERENTIAL EQUATIONS

2020 ◽  
Vol 25 (4) ◽  
pp. 642-660
Author(s):  
Kishor D. Kucche ◽  
Jyoti P. Kharade ◽  
J. Vanterler da C. Sousa
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Fractional Differential

In this paper, we consider the nonlinear Ψ-Hilfer impulsive fractional differential equation. Our main objective is to derive the formula for the solution and examine the existence and uniqueness of solutions. The acquired results are extended to the nonlocal Ψ-Hilfer impulsive fractional differential equation. We gave an applications to the outcomes we obtained. Further, examples are provided in support of the results we got.

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.

Sign in / Sign up

Export Citation Format

Share Document