scholarly journals Multiple Positive Solutions for Quadratic Integral Equations of Fractional Order

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Hui-Sheng Ding ◽  
Man-Man Liu ◽  
Juan J. Nieto
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Positive Solutions ◽  
Fractional Order ◽  
Multiple Solutions ◽  
Fixed Point Theorems ◽  
Multiple Positive Solutions ◽  
Quadratic Integral Equation ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

In this paper, the existence of multiple positive solutions for a class of quadratic integral equation of fractional order is obtained, by utilizing Avery-Henderson and Leggett-Williams multiple fixed point theorems on cones. An example is given to illustrate the applicability of our results. We believe that this is a first result concerning the existence of multiple solutions for such quadratic integral equation of fractional order.

scholarly journals Multiple positive solutions for a system of $(p_{1}, p_{2}, p_{3})$-Laplacian Hadamard fractional order BVP with parameters

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sabbavarapu Nageswara Rao ◽  
Abdullah Ali H. Ahmadini
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Laplacian Operator ◽  
Multiple Positive Solutions ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential

AbstractIn this article, we are pleased to investigate multiple positive solutions for a system of Hadamard fractional differential equations with $(p_{1}, p_{2}, p_{3})$ ( p 1 , p 2 , p 3 ) -Laplacian operator. The main results rely on the standard tools of different fixed point theorems. Finally, we demonstrate the application of the obtained results with the aid of examples.

scholarly journals Multiple Positive Solutions of a Second Order Nonlinear Semipositonem-Point Boundary Value Problem on Time Scales

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Chengjun Yuan ◽  
Yongming Liu
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Time Scales ◽  
Dynamic Equation ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Second Order ◽  
Multiple Positive Solutions ◽  
Point Boundary

In this paper, we study a general second-orderm-point boundary value problem for nonlinear singular dynamic equation on time scalesuΔ∇(t)+a(t)uΔ(t)+b(t)u(t)+λq(t)f(t,u(t))=0,t∈(0,1)𝕋,u(ρ(0))=0,u(σ(1))=∑i=1m-2αiu(ηi). This paper shows the existence of multiple positive solutions iffis semipositone and superlinear. The arguments are based upon fixed-point theorems in a cone.

Existence of positive solutions for Riemann–Liouville fractional order three-point boundary value problem

2015 ◽  
Vol 08 (04) ◽  
pp. 1550057 ◽  
Author(s):  
Sabbavarapu Nageswara Rao
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Order ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Point Boundary ◽  
Existence Of Positive Solutions

In this paper, we study the following fractional order three-point boundary value problem [Formula: see text] where [Formula: see text], are the standard Riemann–Liouville fractional order derivatives with [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]: [Formula: see text] is continuous. By using several well-known fixed-point theorems in a cone, the existence of at least one and two positive solutions is obtained. Some examples are presented to illustrate the main results.

scholarly journals Multiple Solutions for an Equation of Kirchhoff Type: Theoretical and Numerical Aspects

2018 ◽  
Vol 19 (3) ◽  
pp. 559
Author(s):  
André Luís Machado Martinez ◽  
Emerson Vitor Castelani ◽  
Glaucia Maria Bressan ◽  
Elenice Weber Stiegelmeier
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Numerical Method ◽  
Positive Solutions ◽  
Point Theorem ◽  
Multiple Solutions ◽  
Nonlinear Boundary ◽  
Multiple Positive Solutions ◽  
Kirchhoff Type

A nonlinear boundary value problem related to an equation of Kirchhoff type is considered. The existence of multiple positive solutions is proved through Avery-Peterson Fixed Point Theorem. A numerical method based on Levenberg-Marquadt algorithm combined with a heuristic process is present in order to align numerical and theoretical aspects.

scholarly journals Multiple positive solutions for singular higher-order semipositone fractional differential equations with p-Laplacian

2020 ◽  
Vol 25 (5) ◽  
Author(s):  
Qiuyan Zhong ◽  
Xingqiu Zhang ◽  
Lufeng Gu ◽  
Lei Lei ◽  
Zengqin Zhao
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Higher Order ◽  
Multiple Positive Solutions ◽  
Height Functions ◽  
Fractional Differential ◽  
Bounded Sets

In this article, together with Leggett–Williams and Guo–Krasnosel’skii fixed point theorems, height functions on special bounded sets are constructed to obtain the existence of at least three positive solutions for some higher-order fractional differential equations with p-Laplacian. The nonlinearity permits singularities both on the time and the space variables, and it also may change its sign.

scholarly journals Chandrasekhar quadratic and cubic integral equations via Volterra-Stieltjes quadratic integral equation

2021 ◽  
Vol 54 (1) ◽  
pp. 25-36
Author(s):  
Ahmed M. A. El-Sayed ◽  
Yasmin M. Y. Omar
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Fractional Order ◽  
Special Cases ◽  
Quadratic Integral Equation ◽  
Quadratic Integral ◽  
Stieltjes Type

Abstract In this work, we study the existence of one and exactly one solution x ∈ C [ 0 , 1 ] x\in C\left[0,1] , for a delay quadratic integral equation of Volterra-Stieltjes type. As special cases we study a delay quadratic integral equation of fractional order and a Chandrasekhar cubic integral equation.

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