scholarly journals Positive Solutions for a System of Coupled Semipositone Fractional Boundary Value Problems with Sequential Fractional Derivatives

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 753
Author(s):  
Johnny Henderson ◽  
Rodica Luca ◽  
Alexandru Tudorache
Keyword(s):  
Positive Solutions ◽  
Fractional Derivatives ◽  
Existence Results ◽  
Existence And Multiplicity ◽  
Nonlinear Alternative ◽  
Singular Nonlinearities ◽  
Coupled Boundary Conditions ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions ◽  
Fractional Boundary Value Problems

We study the existence and multiplicity of positive solutions for a system of Riemann–Liouville fractional differential equations with sequential derivatives, positive parameters and sign-changing singular nonlinearities, subject to nonlocal coupled boundary conditions which contain Riemann–Stieltjes integrals and various fractional derivatives. In the proof of our main existence results we use the nonlinear alternative of Leray–Schauder type and the Guo–Krasnosel’skii fixed point theorem.

scholarly journals Existence of Positive Solutions for a System of Singular Fractional Boundary Value Problems with p-Laplacian Operators

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1890
Author(s):  
Ahmed Alsaedi ◽  
Rodica Luca ◽  
Bashir Ahmad
Keyword(s):  
Positive Solutions ◽  
Fractional Derivatives ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence And Multiplicity ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions ◽  
Laplacian Operators ◽  
Fractional Boundary Value Problems

We investigate the existence and multiplicity of positive solutions for a system of Riemann–Liouville fractional differential equations with singular nonnegative nonlinearities and p-Laplacian operators, subject to nonlocal boundary conditions which contain fractional derivatives and Riemann–Stieltjes integrals.

scholarly journals Positive Solutions of a Singular Fractional Boundary Value Problem with r-Laplacian Operators

2021 ◽  
Vol 6 (1) ◽  
pp. 18
Author(s):  
Alexandru Tudorache ◽  
Rodica Luca
Keyword(s):  
Positive Solutions ◽  
Fractional Derivatives ◽  
Fractional Integrals ◽  
Fractional Boundary Value Problem ◽  
Existence And Multiplicity ◽  
Singular Nonlinearities ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions ◽  
Laplacian Operators ◽  
Cone Expansion And Compression

We investigate the existence and multiplicity of positive solutions for a system of Riemann–Liouville fractional differential equations with r-Laplacian operators and nonnegative singular nonlinearities depending on fractional integrals, supplemented with nonlocal uncoupled boundary conditions which contain Riemann–Stieltjes integrals and various fractional derivatives. In the proof of our main results we apply the Guo–Krasnosel’skii fixed point theorem of cone expansion and compression of norm type.

scholarly journals Existence of multiple positive solutions for semipositone fractional boundary value problems

Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 749-759 ◽  
Author(s):  
Şerife Ege ◽  
Fatma Topal
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
Existence And Multiplicity ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions ◽  
Fractional Boundary Value Problems

In this paper, we study the existence and multiplicity of positive solutions to the four-point boundary value problems of nonlinear semipositone fractional differential equations. Our results extend some recent works in the literature.

scholarly journals Existence and multiplicity of positive solutions for a singular Riemann-Liouville fractional differential problem

Filomat ◽  
2020 ◽  
Vol 34 (12) ◽  
pp. 3931-3942
Author(s):  
Rodica Luca
Keyword(s):  
Positive Solutions ◽  
Fractional Derivatives ◽  
Fixed Point Index ◽  
Index Theory ◽  
Point Index ◽  
Differential Problem ◽  
Existence And Multiplicity ◽  
Fixed Point Index Theory ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions

We investigate the existence and multiplicity of positive solutions for a nonlinear Riemann-Liouville fractional differential equation with a nonnegative singular nonlinearity, subject to Riemann-Stieltjes boundary conditions which contain fractional derivatives. In the proofs of our main results, we use an application of the Krein-Rutman theorem and some theorems from the fixed point index theory.

scholarly journals Positive Solutions for a Class of Nonlinear Singular Fractional Differential Systems with Riemann–Stieltjes Coupled Integral Boundary Value Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 107
Author(s):  
Daliang Zhao ◽  
Juan Mao
Keyword(s):  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Integral Boundary ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Existence And Multiplicity ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions

In this paper, sufficient conditions ensuring existence and multiplicity of positive solutions for a class of nonlinear singular fractional differential systems are derived with Riemann–Stieltjes coupled integral boundary value conditions in Banach Spaces. Nonlinear functions f(t,u,v) and g(t,u,v) in the considered systems are allowed to be singular at every variable. The boundary conditions here are coupled forms with Riemann–Stieltjes integrals. In order to overcome the difficulties arising from the singularity, a suitable cone is constructed through the properties of Green’s functions associated with the systems. The main tool used in the present paper is the fixed point theorem on cone. Lastly, an example is offered to show the effectiveness of our obtained new results.

scholarly journals Positive solutions for a system of fractional differential equations with p-Laplacian operator and multi-point boundary conditions

2018 ◽  
Vol 23 (5) ◽  
pp. 771-801 ◽  
Author(s):  
Rodica Luca
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Existence Results ◽  
Laplacian Operator ◽  
Point Boundary ◽  
Existence And Nonexistence ◽  
Fractional Differential

>We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann–Liouville fractional differential equations with parameters and p-Laplacian operator subject to multi-point boundary conditions, which contain fractional derivatives. The proof of our main existence results is based on the Guo–Krasnosel'skii fixed-point theorem.

Positive solutions for a system of nonlocal fractional boundary value problems

2013 ◽  
Vol 16 (4) ◽  
Author(s):  
Johnny Henderson ◽  
Rodica Luca
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Existence Results ◽  
Hammerstein Integral Equations ◽  
Existence Of Positive Solutions ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential ◽  
Fractional Boundary Value Problems

AbstractWe investigate the existence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations, subject to multipoint boundary conditions. Existence results for systems of nonlinear Hammerstein integral equations are also presented. Some nontrivial examples are included.

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