scholarly journals Existence and Uniqueness of Positive Solutions for a Class of Nonlinear Fractional Differential Equations with Singular Boundary Value Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yan Debao
Keyword(s):  
Fixed Point ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Nonlinear Function ◽  
Monotone Operators ◽  
Singular Boundary ◽  
Temporal Variables ◽  
Fractional Differential ◽  
Mixed Monotone Operators

This paper focuses on a singular boundary value (SBV) problem of nonlinear fractional differential (NFD) equation defined as follows: D 0 + β υ τ + f τ , υ τ = 0 , τ ∈ 0,1 , υ 0 = υ ′ 0 = υ ″ 0 = υ ″ 1 = 0 , where 3 < β ≤ 4 , D 0 + β is the standard Riemann–Liouville fractional (RLF) derivative. The nonlinear function f τ , υ τ might be singular on the spatial and temporal variables. This paper proves that a positive solution to the SBV problem exists and is unique, taking advantage of Green’s function through a fixed-point (FP) theory on cones and mixed monotone operators.

Existence and uniqueness of positive solutions for boundary value problems of fractional differential equations

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2675-2682 ◽  
Author(s):  
Hojjat Afshari ◽  
Hamidreza Marasi ◽  
Hassen Aydi
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Monotone Operators ◽  
Fractional Differential ◽  
Mixed Monotone Operators

By using fixed point results of mixed monotone operators on cones and the concept of ?-concavity, we study the existence and uniqueness of positive solutions for some nonlinear fractional differential equations via given boundary value problems. Some concrete examples are also provided illustrating the obtained results.

scholarly journals Existence and Uniqueness Results for Two-Term Nonlinear Fractional Differential Equations via a Fixed Point Technique

2021 ◽  
Vol 2021 ◽  
pp. 1-7 ◽  
Author(s):  
H. R. Marasi ◽  
H. Aydi
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Monotone Operators ◽  
Nonlinear Fractional Differential Equations ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Wide Range ◽  
Fractional Differential

The work addressed in this paper is to ensure the existence and uniqueness of positive solutions for initial value problems for nonlinear fractional differential equations with two terms of fractional orders. By virtue of recent fixed point theorems on mixed monotone operators, we get some new straightforward results with a wide range of applications.

scholarly journals Solutions for a category of singular nonlinear fractional differential equations subject to integral boundary conditions

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Debao Yan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Nonlinear Function ◽  
Integral Boundary Conditions ◽  
Singular Boundary ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Uniqueness Of A Solution

AbstractWe concentrate on a category of singular boundary value problems of fractional differential equations with integral boundary conditions, in which the nonlinear function f is singular at $t=0$ t = 0 , 1. We use Banach’s fixed-point theorem and Hölder’s inequality to verify the existence and uniqueness of a solution. Moreover, also we prove the existence of solutions by Krasnoselskii’s and Schaefer’s fixed point theorems.

scholarly journals Existence of the Unique Nontrivial Solution for Mixed Fractional Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Yujing Liu ◽  
Chenguang Yan ◽  
Weihua Jiang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Monotone Operators ◽  
Uniqueness Of The Solution ◽  
Fractional Differential ◽  
The Fixed Point Theorem ◽  
Mixed Monotone Operators

In this paper, we consider the differential equations with right-sided Caputo and left-sided Riemann-Liouville fractional derivatives. Furthermore, the expression of Green’s function is derived, and its properties are investigated. By the fixed-point theorem for both φ − h , e -concave operators and mixed monotone operators, we get the existence and uniqueness of the solution, respectively. As applications, some examples are provided to illustrate our main results.

scholarly journals Analysis of boundary value problem with multi-point conditions involving Caputo-Hadamard fractional derivative

2020 ◽  
Vol 39 (6) ◽  
pp. 1555-1575
Author(s):  
Muthaiah Subramanian ◽  
Thangaraj Nandha Gopal
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Fractional Differential

We study the boundary value problems (BVPs) of the Caputo-Hadamard type fractional differential equations (FDEs) supplemented by multi-point conditions. Many new results of existence and uniqueness are obtained with the use of fixed point theorems for single-valued maps. With the help of examples, the results are well illustrated.

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