The theorem existence and uniqueness of the solution of a fractional differential equation

Banach Theorem ◽

This article aims to demonstrate, using the Picard-Banach theorem, the proof of the theorem-based existence and uniqueness of the solution of an fractional orden differential equation with a fractional Caputo-type derivative.

Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

Advances in Difference Equations ◽

10.1186/s13662-020-02887-4 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Idris Ahmed ◽

Poom Kumam ◽

Jamilu Abubakar ◽

Piyachat Borisut ◽

Kanokwan Sitthithakerngkiet

Keyword(s):

Differential Equation ◽

Boundary Condition ◽

Fixed Point ◽

Periodic Boundary Condition ◽

Periodic Boundary ◽

Fixed Point Theorems ◽

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

A constant enclosure method for validating existence and uniqueness of the solution of an initial value problem for a fractional differential equation

Applied Mathematics and Computation ◽

10.1016/j.amc.2010.07.015 ◽

2010 ◽

Vol 217 (5) ◽

pp. 2162-2168 ◽

Cited By ~ 7

Author(s):

M. Amairi ◽

M. Aoun ◽

S. Najar ◽

M.N. Abdelkrim

Keyword(s):

Differential Equation ◽

Initial Value Problem ◽

Initial Value ◽

Enclosure Method ◽

New Fixed Point Theorems in Orthogonal F -Metric Spaces with Application to Fractional Differential Equation

Symmetry ◽

10.3390/sym12050832 ◽

2020 ◽

Vol 12 (5) ◽

pp. 832

Author(s):

Tanzeela Kanwal ◽

Azhar Hussain ◽

Hamid Baghani ◽

Manuel de la Sen

Keyword(s):

Differential Equation ◽

Fixed Point ◽

Periodic Point ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Nonlinear Fractional Differential Equation ◽

We present the notion of orthogonal F -metric spaces and prove some fixed and periodic point theorems for orthogonal ⊥ Ω -contraction. We give a nontrivial example to prove the validity of our result. Finally, as application, we prove the existence and uniqueness of the solution of a nonlinear fractional differential equation.

Existence and uniqueness of the solution to uncertain fractional differential equation

Journal of Uncertainty Analysis and Applications ◽

10.1186/s40467-015-0028-6 ◽

2015 ◽

Vol 3 (1) ◽

Cited By ~ 9

Author(s):

Yuanguo Zhu

Keyword(s):

Differential Equation ◽

Existence, Uniqueness, and Eq–Ulam-Type Stability of Fuzzy Fractional Differential Equation

Fractal and Fractional ◽

10.3390/fractalfract5030066 ◽

2021 ◽

Vol 5 (3) ◽

pp. 66

Author(s):

Azmat Ullah Khan Niazi ◽

Jiawei He ◽

Ramsha Shafqat ◽

Bilal Ahmed

Keyword(s):

Differential Equation ◽

Cauchy Problem ◽

Fuzzy Fractional Differential Equation

Initial Conditions ◽

The Cauchy Problem ◽

Fractional Differential ◽

Ulam Type Stability ◽

Fuzzy Fractional Differential Equations ◽

This paper concerns with the existence and uniqueness of the Cauchy problem for a system of fuzzy fractional differential equation with Caputo derivative of order q∈(1,2], 0cD0+qu(t)=λu(t)⊕f(t,u(t))⊕B(t)C(t),t∈[0,T] with initial conditions u(0)=u0,u′(0)=u1. Moreover, by using direct analytic methods, the Eq–Ulam-type results are also presented. In addition, several examples are given which show the applicability of fuzzy fractional differential equations.

Existence and uniqueness of positive solutions for a class of fractional differential equation with integral boundary conditions

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2017.2.2 ◽

2017 ◽

Vol 22 (2) ◽

pp. 160-172 ◽

Cited By ~ 7

Author(s):

Haixing Feng ◽

◽

Chengbo Zhai ◽

Keyword(s):

Differential Equation ◽

Boundary Conditions ◽

Positive Solutions ◽

Integral Boundary Conditions ◽

Integral Boundary ◽

Existence and uniqueness of positive solutions to m-point boundary value problem for nonlinear fractional differential equation

Journal of Applied Mathematics and Computing ◽

10.1007/s12190-011-0475-2 ◽

2011 ◽

Vol 38 (1-2) ◽

pp. 225-241 ◽

Cited By ~ 9

Author(s):

Sihua Liang ◽

Jihui Zhang

Keyword(s):

Differential Equation ◽

Boundary Value Problem ◽

Positive Solutions ◽

Boundary Value ◽

Point Boundary ◽

Nonlinear Fractional Differential Equation ◽

Mixed monotone operator methods for the existence and uniqueness of positive solutions to Riemann-Liouville fractional differential equation boundary value problems

Boundary Value Problems ◽

10.1186/1687-2770-2013-85 ◽

2013 ◽

Vol 2013 (1) ◽

Cited By ~ 9

Author(s):

Chengbo Zhai ◽

Mengru Hao

Keyword(s):

Differential Equation ◽

Boundary Value Problems ◽

Positive Solutions ◽

Monotone Operator ◽

Boundary Value ◽

Mixed Monotone Operator ◽

Equation Boundary ◽

Initial boundary value problems for a fractional differential equation with hyper-Bessel operator

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2018-0013 ◽

2018 ◽

Vol 21 (1) ◽

pp. 200-219 ◽

Cited By ~ 4

Author(s):

Fatma Al-Musalhi ◽

Nasser Al-Salti ◽

Erkinjon Karimov

Keyword(s):

Differential Equation ◽

Initial Boundary ◽

Fractional Diffusion ◽

Initial Boundary Value Problems ◽

Bessel Differential Operator ◽

Fractional Differential ◽

Inverse Source Problems ◽

Initial Boundary Value

AbstractDirect and inverse source problems of a fractional diffusion equation with regularized Caputo-like counterpart of a hyper-Bessel differential operator are considered. Solutions to these problems are constructed based on appropriate eigenfunction expansions and results on existence and uniqueness are established. To solve the resultant equations, a solution to such kind of non-homogeneous fractional differential equation is also presented.