scholarly journals Positive solutions of boundary value problems for p-Laplacian fractional differential equations

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1265-1277 ◽  
Author(s):  
Fatma Fen ◽  
Ilkay Karac ◽  
Ozlem Ozen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Laplacian Operator ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

This work is devoted to the existence of positive solutions for nonlinear fractional differential equations with p-Laplacian operator. By using five functionals fixed point theorem, the existence of at least three positive solutions are obtained. As an application, an example is presented to demonstrate our main result.

scholarly journals Positive Solutions for a System of Fractional Differential Equations with Two Parameters

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Hongyu Li ◽  
Junting Zhang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Positive Solutions ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Laplacian Operator ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
Two Parameters

In this paper, the existence of positive solutions in terms of different values of two parameters for a system of conformable-type fractional differential equations with the p-Laplacian operator is obtained via Guo-Krasnosel’skii fixed point theorem.

scholarly journals Existence of positive solutions for a system of nonlinear Caputo type fractional differential equations with two parameters

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yang Chen ◽  
Hongyu Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Positive Solutions ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Existence Theorems ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
Two Parameters

AbstractThe main purpose of this paper is to prove the existence of positive solutions for a system of nonlinear Caputo-type fractional differential equations with two parameters. By using the Guo–Krasnosel’skii fixed point theorem, some existence theorems of positive solutions are obtained in terms of different values of parameters. Two examples are given to illustrate the main results.

scholarly journals The Existence of Positive Solutions for Fractional Differential Equations with Sign Changing Nonlinearities

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Weihua Jiang ◽  
Jiqing Qiu ◽  
Weiwei Guo
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Eigenvalue Problems ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
Generalized Boundary Conditions

We investigate the existence of at least two positive solutions to eigenvalue problems of fractional differential equations with sign changing nonlinearities in more generalized boundary conditions. Our analysis relies on the Avery-Peterson fixed point theorem in a cone. Some examples are given for the illustration of main results.

scholarly journals Existence of Positive Solutions for a Class of Delay Fractional Differential Equations with Generalization to N-Term

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Azizollah Babakhani ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Initial Conditions ◽  
Banach Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

We established the existence of a positive solution of nonlinear fractional differential equationsL(D)[x(t)−x(0)]=f(t,xt),t∈(0,b]with finite delayx(t)=ω(t),t∈[−τ,0], wherelimt→0f(t,xt)=+∞, that is,fis singular att=0andxt∈C([−τ,0],ℝ≥0). The operator ofL(D)involves the Riemann-Liouville fractional derivatives. In this problem, the initial conditions with fractional order and some relations among them were considered. The analysis rely on the alternative of the Leray-Schauder fixed point theorem, the Banach fixed point theorem, and the Arzela-Ascoli theorem in a cone.

scholarly journals Existence criteria of positive solutions for fractional p-Laplacian boundary value problems

Filomat ◽  
2020 ◽  
Vol 34 (11) ◽  
pp. 3789-3799
Author(s):  
Deren Yoruk ◽  
Tugba Cerdik ◽  
Ravi Agarwal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Existence Of Positive Solutions ◽  
Existence Criteria

By means of the Bai-Ge?s fixed point theorem, this paper shows the existence of positive solutions for nonlinear fractional p-Laplacian differential equations. Here, the fractional derivative is the standard Riemann-Liouville one. Finally, an example is given to illustrate the importance of results obtained.

Positive solutions for fractional differential equations with non-separated type nonlocal multi-point and multi-term integral boundary conditions

2021 ◽  
Vol 66 (4) ◽  
pp. 691-708
Author(s):  
Habib Djourdem ◽  
◽  
Slimane Benaicha ◽  
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Positive Solutions ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fractional Differential

In this paper, we investigate a class of nonlinear fractional differential equations that contain both the multi-term fractional integral boundary condition and the multi-point boundary condition. By the Krasnoselskii fixed point theorem we obtain the existence of at least one positive solution. Then, we obtain the existence of at least three positive solutions by the Legget-Williams fixed point theorem. Two examples are given to illustrate our main results.

scholarly journals Analysis of Implicit Type Nonlinear Dynamical Problem of Impulsive Fractional Differential Equations

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Naveed Ahmad ◽  
Zeeshan Ali ◽  
Kamal Shah ◽  
Akbar Zada ◽  
Ghaus ur Rahman
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Nonlocal Boundary ◽  
Dynamical Problem ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

We study the existence, uniqueness, and various kinds of Ulam–Hyers stability of the solutions to a nonlinear implicit type dynamical problem of impulsive fractional differential equations with nonlocal boundary conditions involving Caputo derivative. We develop conditions for uniqueness and existence by using the classical fixed point theorems such as Banach fixed point theorem and Krasnoselskii’s fixed point theorem. For stability, we utilized classical functional analysis. Also, an example is given to demonstrate our main theoretical results.

scholarly journals Existence and Kummer Stability for a System of Nonlinear ϕ-Hilfer Fractional Differential Equations with Application

2021 ◽  
Vol 5 (4) ◽  
pp. 200
Author(s):  
Fatemeh Mottaghi ◽  
Chenkuan Li ◽  
Thabet Abdeljawad ◽  
Reza Saadati ◽  
Mohammad Bagher Ghaemi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Biological Systems ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Differential

Using Krasnoselskii’s fixed point theorem and Arzela–Ascoli theorem, we investigate the existence of solutions for a system of nonlinear ϕ-Hilfer fractional differential equations. Moreover, applying an alternative fixed point theorem due to Diaz and Margolis, we prove the Kummer stability of the system on the compact domains. We also apply our main results to study the existence and Kummer stability of Lotka–Volterra’s equations that are useful to describe and characterize the dynamics of biological systems.

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