Existence and iteration of positive solutions for high-order fractional differential equations with integral conditions on a half-line

Zhang, Xingqiu

doi:10.1007/s12190-013-0715-8

Cited by 5 publications

(1 citation statement)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As it has been stated in Sun and Zhao (2014), Zhang (2014), Cabada and Hamdi (2014), Zhao, Chai and Ge (2013), and Jiang and Zhong (2014), this type of conditions appear in different real phenomena, e.g., blood flow problems, chemical engineering, thermoelasticity and population dynamics.…”

Section: Introductionmentioning

confidence: 86%

Existence and non-existence of positive solutions for integral boundary value problems of high-order fractional differential equations with generalised p-Laplacian operator

Sun

Chen

2017

IJDSDE

View full text Add to dashboard Cite

Abstract:In this paper, we investigate the non-linear integral boundary value problem of fractional differential equations with generalised p-Laplacian operator. By means of the monotone iteration method, we obtain the existence of positive solutions and establish the iterative sequence for approximating the solutions. Moreover, the non-existence of positive solution is also considered. An example is given to show the applicability of our main results.

show abstract

Section: Introductionmentioning

confidence: 86%

Existence and non-existence of positive solutions for integral boundary value problems of high-order fractional differential equations with generalised p-Laplacian operator

Sun

Chen

2017

IJDSDE

View full text Add to dashboard Cite

show abstract

Existence results for the generalized Riemann–Liouville type fractional Fisher‐like equation on the half‐line

Nyamoradi,

Ahmad

2024

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we discuss the existence of multiplicity of positive solutions to a new generalized Riemann–Liouville type fractional Fisher‐like equation on a semi‐infinite interval equipped with nonlocal multipoint boundary conditions involving Riemann–Liouville fractional derivative and integral operators. The existence of at least two positive solutions for the given problem is established by using the concept of complete continuity and iterative positive solutions. We show the existence of at least three positive solutions to the problem at hand by applying the generalized Leggett–Williams fixed‐point theorem due to Bai and Ge [Z. Bai, B. Ge, Existence of three positive solutions for some second‐order boundary value problems, Comput. Math. Appl. 48 (2014) 699‐70]. Illustrative examples are constructed to demonstrate the effectiveness of the main results. It has also been indicated in Section 5 that some new results appear as special cases by choosing the parameters involved in the given problem appropriately.

show abstract

Successively iterative method for a class of high-order fractional differential equations with multi-point boundary value conditions on half-line

Sun

Han

2016

Bound Value Probl

View full text Add to dashboard Cite

In this paper, we study the existence of the positive solutions for a class of high-order differential equations with multi-point boundary value conditions involving the Caputo fractional derivative on infinite interval. Moreover, we develop two computable explicit monotone iterative sequences for approximating the two minimal and maximal positive solutions. An example is given to show the applicability of our main results. MSC: 34A08; 34B18

show abstract

Existence and iteration of positive solutions for high-order fractional differential equations with integral conditions on a half-line

Cited by 5 publications

References 13 publications

Existence and non-existence of positive solutions for integral boundary value problems of high-order fractional differential equations with generalised p-Laplacian operator

Existence and non-existence of positive solutions for integral boundary value problems of high-order fractional differential equations with generalised p-Laplacian operator

Existence results for the generalized Riemann–Liouville type fractional Fisher‐like equation on the half‐line

Successively iterative method for a class of high-order fractional differential equations with multi-point boundary value conditions on half-line

Contact Info

Product

Resources

About