Applications of a Fixed Point Result for Solving Nonlinear Fractional and Integral Differential Equations

Guran, Liliana; Mitrović, Zoran D.; Reddy, G. Sudhaamsh Mohan; Belhenniche, Abdelkader; Radenović, Stojan

doi:10.3390/fractalfract5040211

Cited by 15 publications

(8 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Vector-valued spaces and Perov-type problems were treated in [127,128]. F-contractions in metric-like and b-metric-like spaces were under investigation in [9,[129][130][131][132][133][134][135]. Partial metric spaces and F-contractions in them were treated in [136][137][138][139][140][141].…”

Section: Some Other Areas Of Researchmentioning

confidence: 99%

On F-Contractions: A Survey

Fabiano

Kadelburg

Mirkov

et al. 2022

Contemporary Mathematics

Self Cite

View full text Add to dashboard Cite

D. Wardowski proved in 2012 a generalization of Banach Contraction Principle by introducing F-contractions in metric spaces. In the next ten years, a great number of researchers used Wardowski's approach, or some of its modifications, to obtain new fixed point results for single- and multivalued mappings in various kinds of spaces. In this review article, we present a survey of these investigations, including some improvements, in particular concerning conditions imposed on function F entering the contractive condition.

show abstract

Section: Some Other Areas Of Researchmentioning

confidence: 99%

On F-Contractions: A Survey

Fabiano

Kadelburg

Mirkov

et al. 2022

Contemporary Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Fixed-point theorems for monotone nonexpansive mappings in ordered metric spaces have been widely investigated and have found various applications in matrix equations and differential and integral equations [14,26,29,30,[38][39][40]. In this section we discuss the existence of solutions of initial-value problems for nonlinear first-order ordinary differential equations.…”

Section: Application To Initial-value Problemsmentioning

confidence: 99%

“…The contractivity criterion on the nonlinear map is only considered to hold elements that are comparable in the partial order in such findings. The reader is directed to the ground-breaking work on the subject, which has applications in integral, differential, and nonlinear fractional evolution equations and equilibrium problems; see [2,[25][26][27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

A Krasnoselskii–Ishikawa Iterative Algorithm for Monotone Reich Contractions in Partially Ordered Banach Spaces with an Application

2021

View full text Add to dashboard Cite

Iterative algorithms have been utilized for the computation of approximate solutions of stationary and evolutionary problems associated with differential equations. The aim of this article is to introduce concepts of monotone Reich and Chatterjea nonexpansive mappings on partially ordered Banach spaces. We describe sufficient conditions for the existence of an approximate fixed-point sequence (AFPS) and prove certain fixed-point results using the Krasnoselskii–Ishikawa iterative algorithm. Moreover, we present some interesting examples to highlight the superiority of our results. Lastly, we provide both weak and strong convergence results for such mappings and consider an application of our results to prove the existence of a solution to an initial value problem.

show abstract

“…Lately, various types of Hermite-Hadamard type inequalities have been studied and generalized for different types of convex functions under different conditions and parameters. For more information, see [11][12][13][14][15][16] and the references therein. The fractional calculus used in the paper is an extension of the standard calculus, where we define the integral and the derivative for a fractional number.…”

Section: Introductionmentioning

confidence: 99%

Hermite–Hadamard Type Inequalities Involving (k-p) Fractional Operator for Various Types of Convex Functions

Stojiljković

Ramaswamy²,

Alshammari³

et al. 2022

Fractal Fract

Self Cite

View full text Add to dashboard Cite

We establish various fractional convex inequalities of the Hermite–Hadamard type with addition to many other inequalities. Various types of such inequalities are obtained, such as (p,h) fractional type inequality and many others, as the (p,h)-convexity is the generalization of the other convex inequalities. As a consequence of the (h,m)-convexity, the fractional inequality of the (s,m)-type is obtained. Many consequences of such fractional inequalities and generalizations are obtained.

show abstract

Applications of a Fixed Point Result for Solving Nonlinear Fractional and Integral Differential Equations

Abstract: In this article, we apply one fixed point theorem in the setting of b-metric-like spaces to prove the existence of solutions for one type of Caputo fractional differential equation as well as the existence of solutions for one integral equation created in mechanical engineering.

Cited by 15 publications

References 32 publications

On F-Contractions: A Survey

On F-Contractions: A Survey

A Krasnoselskii–Ishikawa Iterative Algorithm for Monotone Reich Contractions in Partially Ordered Banach Spaces with an Application

Hermite–Hadamard Type Inequalities Involving (k-p) Fractional Operator for Various Types of Convex Functions

Contact Info

Product

Resources

About