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 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.

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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