The eigenvalue for a class of singular p-Laplacian fractional differential equations involving the Riemann–Stieltjes integral boundary condition

2014 ◽  
Vol 235 ◽  
pp. 412-422 ◽  
Author(s):  
Xinguang Zhang ◽  
Lishan Liu ◽  
Benchawan Wiwatanapataphee ◽  
Yonghong Wu
Keyword(s):  
Boundary Condition ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Integral Boundary Condition ◽  
Stieltjes Integral ◽  
Integral Boundary ◽  
Fractional Differential

Existence and uniqueness results for Riemann–Stieltjes integral boundary value problems of nonlinear implicit Hadamard fractional differential equations

2021 ◽  
Author(s):  
Mohamed I. Abbas
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Stieltjes Integral ◽  
Integral Boundary ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential ◽  
Integral Boundary Value Problems

In this paper, we study the existence and uniqueness of solutions for Riemann–Stieltjes integral boundary value problems of nonlinear implicit Hadamard fractional differential equations. The investigation of the main results depends on Schauder’s fixed point theorem and Banach’s contraction principle. An illustrative example is given to show the applicability of theoretical results.

scholarly journals Existence and Uniqueness of Positive Solutions for a New System of Fractional Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Hongyu Li ◽  
Yang Chen
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Integral Boundary Conditions ◽  
Stieltjes Integral ◽  
Integral Boundary ◽  
Fractional Differential ◽  
New System

By virtue of a recent existing fixed point theorem of increasing φ−h,e-concave operator by Zhai and Wang, we consider the existence and uniqueness of positive solutions for a new system of Caputo-type fractional differential equations with Riemann–Stieltjes integral boundary conditions.

scholarly journals The Extremal Solution To Conformable Fractional Differential Equations Involving Integral Boundary Condition

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 186 ◽  
Author(s):  
Shuman Meng ◽  
Yujun Cui
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Integral Boundary Conditions ◽  
Lower Solution ◽  
Stieltjes Integral ◽  
Integral Boundary ◽  
First Order ◽  
Monotone Iterative ◽  
Fractional Differential

In this article, by using the monotone iterative technique coupled with the method of upper and lower solution, we obtain the existence of extremal iteration solutions to conformable fractional differential equations involving Riemann-Stieltjes integral boundary conditions. At the same time, the comparison principle of solving such problems is investigated. Finally, an example is given to illustrate our main results. It should be noted that the conformal fractional derivative is essentially a modified version of the first-order derivative. Our results show that such known results can be translated and stated in the setting of the so-called conformal fractional derivative.

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 Existence of Positive Solution for Semipositone Fractional Differential Equations Involving Riemann-Stieltjes Integral Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Wei Wang ◽  
Li Huang
Keyword(s):  
Differential Equations ◽  
Positive Solution ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Stieltjes Integral ◽  
Integral Conditions ◽  
Technical Approach ◽  
Integral Boundary ◽  
Fractional Differential

The existence of at least one positive solution is established for a class of semipositone fractional differential equations with Riemann-Stieltjes integral boundary condition. The technical approach is mainly based on the fixed-point theory in a cone.

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