scholarly journals On strong singular fractional version of the Sturm–Liouville equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mehdi Shabibi ◽  
Akbar Zada ◽  
Hashem Parvaneh Masiha ◽  
Shahram Rezapour
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Liouville Equation ◽  
Existence Of Solutions ◽  
Integral Boundary Conditions ◽  
Initial Condition ◽  
Integral Boundary ◽  
Sturm Liouville

AbstractThe Sturm–Liouville equation is among the significant differential equations having many applications, and a lot of researchers have studied it. Up to now, different versions of this equation have been reviewed, but one of its most attractive versions is its strong singular version. In this work, we investigate the existence of solutions for the strong singular version of the fractional Sturm–Liouville differential equation with multi-points integral boundary conditions. Also, the continuity depending on coefficients of the initial condition of the equation is examined. An example is proposed to demonstrate our main result.

Existence of solutions for sequential fractional differential equations with four-point nonlocal fractional integral boundary conditions

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Bashir Ahmad ◽  
Ahmed Alsaedi ◽  
Hana Al-Hutami
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fractional Integral ◽  
Existence Of Solutions ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

AbstractThis paper investigates the existence of solutions for a nonlinear boundary value problem of sequential fractional differential equations with four-point nonlocal Riemann-Liouville type fractional integral boundary conditions. We apply Banach’s contraction principle and Krasnoselskii’s fixed point theorem to establish the existence of results. Some illustrative examples are also presented.

scholarly journals Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hui Li ◽  
Libo Wang ◽  
Minghe Pei
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fourth Order Differential Equation

We investigate the existence of solutions and positive solutions for a nonlinear fourth-order differential equation with integral boundary conditions of the formx(4)(t)=f(t,x(t),x′(t),x′′(t),x′′′(t)),t∈[0,1],x(0)=x′(1)=0,x′′(0)=∫01h(s,x(s),x′(s),x′′(s))ds,x′′′(1)=0, wheref∈C([0,1]×ℝ4),h∈C([0,1]×ℝ3). By using a fixed point theorem due to D. O'Regan, the existence of solutions and positive solutions for the previous boundary value problems is obtained. Meanwhile, as applications, some examples are given to illustrate our results.

scholarly journals Multi-Term Fractional Differential Equations with Generalized Integral Boundary Conditions

2019 ◽  
Vol 3 (3) ◽  
pp. 44
Author(s):  
Bashir Ahmad ◽  
Madeaha Alghanmi ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equation ◽  
Functional Analysis ◽  
Boundary Conditions ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Integral Boundary Conditions ◽  
Nonlinear Fractional Differential Equation ◽  
Integral Boundary ◽  
Fractional Differential

We discuss the existence of solutions for a Caputo type multi-term nonlinear fractional differential equation supplemented with generalized integral boundary conditions. The modern tools of functional analysis are applied to achieve the desired results. Examples are constructed for illustrating the obtained work. Some new results follow as spacial cases of the ones reported in this paper.

scholarly journals The Existence Results of Solutions for System of Fractional Differential Equations with Integral Boundary Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Dongxia Zan ◽  
Run Xu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Initial Point ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Integral Boundary ◽  
Fractional Differential System ◽  
Fractional Differential

In this paper, we investigated the system of fractional differential equations with integral boundary conditions. By using a fixed point theorem in the Banach spaces, we get the existence of solutions for the fractional differential system. By constructing iterative sequences for any given initial point in space, we can approximate this solution. As an application, an example is presented to illustrate our main results.

scholarly journals A second order differential equation with generalized Sturm-Liouville integral boundary conditions at resonance

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1437-1444 ◽  
Author(s):  
Zengji Du ◽  
Jian Yin
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Nonlinear Differential Equations ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Integral Boundary Conditions ◽  
Second Order ◽  
Integral Boundary ◽  
At Resonance ◽  
Sturm Liouville

By using Mawhin coincidence degree theory, we investigate the existence of solutions for a class of second order nonlinear differential equations with generalized Sturm-Liouville integral boundary conditions at resonance. The results extend some known conclusions of integral boundary value problem at resonance for nonlinear differential equations

scholarly journals On the Existence of Solutions for Impulsive Fractional Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Yongliang Guan ◽  
Zengqin Zhao ◽  
Xiuli Lin
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solution ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Global Bifurcation ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

We are concerned with a type of impulsive fractional differential equations attached with integral boundary conditions and get the existence of at least one positive solution via global bifurcation techniques.

Sign in / Sign up

Export Citation Format

Share Document