Our aim in this paper is to study the existence of solution sets and its topological structure for non-localfractional differential equations on half-line a Banach space using Riemann-Liouville definition. Themain result based Meir-Keeler fixed point theorem condensing operators combined with measure ofnon-compactness. An example given illustrate feasibility our main result.

*Correspondence: [email protected] 1Department of Quantitative Methods for Economics and Business, University of Granada, Granada, Spain Full list of author information is available at the end of the article Abstract Very recently, Roldán-López-de-Hierro and Shahzad introduced the notion of R-contractions as an extension of several notions given by different researchers (for instance, R-contractio...

Recently, a class of mappings named as couplings was introduced in [U.P.B. Sci. Bull. Series A, 79 (2017), 1-12]. Based on this concept, we introduce symmetric Meir-Keeler and ensure the existence strong coupled fixed points. We present some concrete examples to support obtained results. Furthermore, an application our results, investigate unique solution system integral equations.

The study of random fixed point theory was initiated by the Prague school of probabilists in the 1950s [12, 13, 26]. Random fixed point theorems are stochastic generalization of classical fixed point theorems. The survey article by Bharucha-Reid [10] attracted the attention of several mathematicians and gave wings to this theory. Itoh [16] extended Spacek’s and Hans’s theorem to multivalued con...

In this article, we establish certain sufficient conditions to show the existence of solutions a fractional differential equation with ?-Riemann-Liouville and ?-Caputo derivative in special Banach space. Our approach is based on fixed point theorems for Meir-Keeler condensing operators via measure non-compactness. Also an example given illustrate our approach.

In the current contribution, an appropriate quantity connected to space of all convergent sequences is provided and shown be a measure noncompactness in Banach space. Through application fixed point theorems Darbo Meir–Keeler, this amount used discuss whether solution infinite system fractional Sturm–Liouville operators exists. We offer numerical example as key finding study.

Throughout this paper, by R we denote the set of all nonnegative numbers, while N is the set of all natural numbers. Let A and B be nonempty subsets of a metric space X, d . Consider a mapping f : A ∪ B → A ∪ B, f is called a cyclic map if f A ⊆ B and f B ⊆ A. A point x in A is called a best proximity point of f in A if d x, fx d A,B is satisfied, where d A,B inf{d x, y : x ∈ A,y ∈ B}, and x ∈ ...