Some Results on Multipoint Integral Boundary Value Problems for Fractional Integro-Differential Equations

2021 ◽  
Vol 7 (2) ◽  
pp. 127-136
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Integral Boundary ◽  
Integral Boundary Value Problems

Existence of bounded solutions of integral boundary value problems for singular differential equations on whole lines

2014 ◽  
Vol 25 (08) ◽  
pp. 1450078 ◽  
Author(s):  
Yuji Liu ◽  
Shengping Chen
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Nonlinear Operator ◽  
Boundary Value ◽  
Nonnegative Function ◽  
Bounded Solutions ◽  
Integral Boundary ◽  
Singular Differential Equations ◽  
Nonlinear Alternative ◽  
Integral Boundary Value Problems

Boundary value problems of second-order singular differential equations with nonlinear operator Φ on whole lines are discussed. By applying the nonlinear alternative of Leray–Schauder-type fixed point theorem, some existence results of solutions for integral boundary value problems of differential equations on whole lines are established. The emphasis is put on the nonlinear operator [Φ(ρ(t)x′(t))]′ involved with the nonnegative function ρ that may satisfy ρ(0) = 0, the strictly increasing sup-multiplicative-like function Φ and the differential equations are defined on the whole line. Three examples and a remark are presented to illustrate the main theorems.

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.

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