Existence Results For a Ψ-Hilfer Type Nonlocal Fractional Boundary Value Problem via Topological Degree Theory

2021 ◽  
Vol 30 (7) ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K Ntouyas ◽  
Ahmed Alsaedi ◽  
Fawziah M Alotaibi
Keyword(s):  
Boundary Value Problem ◽  
Topological Degree ◽  
Boundary Value ◽  
Degree Theory ◽  
Existence Results ◽  
Fractional Boundary Value Problem ◽  
Topological Degree Theory

scholarly journals Nontrivial Solutions for the 2 n th Lidstone Boundary Value Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Yaohong Li ◽  
Jiafa Xu ◽  
Yongli Zan
Keyword(s):  
Linear Operator ◽  
Boundary Value Problem ◽  
Topological Degree ◽  
Boundary Value ◽  
Degree Theory ◽  
Topological Degree Theory ◽  
Nontrivial Solutions

In this paper, we study the existence of nontrivial solutions for the 2 n th Lidstone boundary value problem with a sign-changing nonlinearity. Under some conditions involving the eigenvalues of a linear operator, we use the topological degree theory to obtain our main results.

scholarly journals Existence Results for Caputo–Hadamard Nonlocal Fractional Multi-Order Boundary Value Problems

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 719
Author(s):  
Shahram Rezapour ◽  
Salim Ben Chikh ◽  
Abdelkader Amara ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon ◽  
...  
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Topological Degree ◽  
Boundary Value ◽  
Existence Results ◽  
Fractional Boundary Value Problem ◽  
New Class

In this paper, we studied the existence results for solutions of a new class of the fractional boundary value problem in the Caputo–Hadamard settings. Moreover, boundary conditions of this fractional problem were formulated as the mixed multi-order Hadamard integro-derivative conditions. To prove the main existence results, we applied two well-known techniques in the topological degree and fixed point theories. Finally, we provide two examples to show the compatibility of our theoretical findings.

scholarly journals A study on multiterm hybrid multi-order fractional boundary value problem coupled with its stability analysis of Ulam–Hyers type

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmed Nouara ◽  
Abdelkader Amara ◽  
Eva Kaslik ◽  
Sina Etemad ◽  
Shahram Rezapour ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Boundary Value Problem ◽  
Fractional Derivatives ◽  
Boundary Value ◽  
Research Work ◽  
Existence Results ◽  
Fractional Boundary Value Problem ◽  
Numerical Examples ◽  
Fractional Derivatives And Integrals ◽  
Fractional Differential

AbstractIn this research work, a newly-proposed multiterm hybrid multi-order fractional boundary value problem is studied. The existence results for the supposed hybrid fractional differential equation that involves Riemann–Liouville fractional derivatives and integrals of multi-orders type are derived using Dhage’s technique, which deals with a composition of three operators. After that, its stability analysis of Ulam–Hyers type and the relevant generalizations are checked. Some illustrative numerical examples are provided at the end to illustrate and validate our obtained results.

scholarly journals Positive Solutions Using Bifurcation Techniques for Boundary Value Problems of Fractional Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yansheng Liu
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Topological Degree ◽  
Boundary Value ◽  
Degree Theory ◽  
Topological Degree Theory ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

This paper is concerned with the existence of positive solutions for a class of boundary value problems of fractional differential equations with parameter. The main tools used here are bifurcation techniques and topological degree theory. Finally, an example is worked out to demonstrate the main result.

scholarly journals Bifurcation from Interval and Positive Solutions of a Nonlinear Second-Order Dynamic Boundary Value Problem on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Hua Luo
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Time Scale ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Global Bifurcation ◽  
Degree Theory ◽  
Second Order ◽  
Topological Degree Theory ◽  
Bifurcation From Interval

Let𝕋be a time scale with0,T∈𝕋. We give a global description of the branches of positive solutions to the nonlinear boundary value problem of second-order dynamic equation on a time scale𝕋,uΔΔ(t)+f(t,uσ(t))=0,  t∈[0,T]𝕋,  u(0)=u(σ2(T))=0, which is not necessarily linearizable. Our approaches are based on topological degree theory and global bifurcation techniques.

scholarly journals Existence problems for homoclinic solutions

2002 ◽  
Vol 7 (1) ◽  
pp. 1-27 ◽  
Author(s):  
Cezar Avramescu
Keyword(s):  
Fixed Point ◽  
Topological Degree ◽  
Degree Theory ◽  
Existence Results ◽  
Fixed Point Method ◽  
Point Method ◽  
Homoclinic Solutions ◽  
Topological Degree Theory

The problemx˙=f(t,x), x(−∞)=x(+∞), wherex(±∞):=limt→±∞x(t)∈ℝn, is considered. Some existence results for this problem are established using the fixed point method and topological degree theory.

scholarly journals Topological essentiality and differential inclusions

1992 ◽  
Vol 45 (2) ◽  
pp. 177-193 ◽  
Author(s):  
Lech Gorniewicz ◽  
Miroslaw Slosarski
Keyword(s):  
Boundary Value Problems ◽  
Large Class ◽  
Differential Inclusion ◽  
Topological Degree ◽  
Differential Inclusions ◽  
Boundary Value ◽  
Degree Theory ◽  
Multivalued Mappings ◽  
Topological Degree Theory ◽  
Lower Semi

In the present paper a concept of topological essentiality for a large class of multivalued mappings is introduced. This concept is strictly related to the Leray-Schauder topological degree theory but is simpler and also more general. Applying the above concept to boundary value problems for differential inclusion with both upper semi-continuous and lower semi-continuous right hand sides, several new results are obtained.

scholarly journals Criteria for existence of solutions for a Liouville–Caputo boundary value problem via generalized Gronwall’s inequality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hakimeh Mohammadi ◽  
Dumitru Baleanu ◽  
Sina Etemad ◽  
Shahram Rezapour
Keyword(s):  
Boundary Value Problem ◽  
Continuous Dependence ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Existence Results ◽  
Fractional Boundary Value Problem ◽  
Gronwall’S Inequality ◽  
The Given ◽  
Continuous Dependence Of Solutions

AbstractIn this research, we first investigate the existence of solutions for a new fractional boundary value problem in the Liouville–Caputo setting with mixed integro-derivative boundary conditions. To do this, Kuratowski’s measure of noncompactness and Sadovskii’s fixed point theorem are our tools to reach this aim. In the sequel, we discuss the continuous dependence of solutions on parameters by means of the generalized Gronwall inequality. Moreover, we consider an inclusion version of the given boundary problem in which we study its existence results by means of the endpoint theory. Finally, we prepare two simulative numerical examples to confirm the validity of the analytical findings.

scholarly journals Existence Results for the Solution of the Hybrid Caputo–Hadamard Fractional Differential Problems Using Dhage’s Approach

2021 ◽  
Vol 6 (1) ◽  
pp. 17
Author(s):  
Muhammad Yaseen ◽  
Sadia Mumtaz ◽  
Reny George ◽  
Azhar Hussain
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Results ◽  
Fractional Boundary Value Problem ◽  
Numerical Examples ◽  
Fractional Differential

In this work, we explore the existence results for the hybrid Caputo–Hadamard fractional boundary value problem (CH-FBVP). The inclusion version of the proposed BVP with a three-point hybrid Caputo–Hadamard terminal conditions is also considered and the related existence results are provided. To achieve these goals, we utilize the well-known fixed point theorems attributed to Dhage for both BVPs. Moreover, we present two numerical examples to validate our analytical findings.

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