scholarly journals Riemann-Stieltjes Integral boundary value problems involving mixed Riemann-Liouville and Caputo fractional derivatives

2021 ◽  
Vol 2021 (1) ◽  
Keyword(s):  
Boundary Value Problems ◽  
Fractional Derivatives ◽  
Boundary Value ◽  
Stieltjes Integral ◽  
Caputo Fractional Derivatives ◽  
Integral Boundary ◽  
Integral Boundary Value Problems

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 Positive Solutions for a System of Fractional Integral Boundary Value Problems Involving Hadamard-Type Fractional Derivatives

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Haiyan Zhang ◽  
Yaohong Li ◽  
Jiafa Xu
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Derivatives ◽  
Fixed Point Index ◽  
Fractional Integral ◽  
Boundary Value ◽  
Integral Boundary ◽  
Existence Of Positive Solutions ◽  
Integral Boundary Value Problems ◽  
Hadamard Fractional Integral

In this paper, we use fixed-point index to study the existence of positive solutions for a system of Hadamard fractional integral boundary value problems involving nonnegative nonlinearities. By virtue of integral-type Jensen inequalities, some appropriate concave and convex functions are used to depict the coupling behaviors for our nonlinearities fii=1, 2.

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