Measure of noncompactness of a new space of tempered sequences and its application on fractional differential equations

Existence and Uniqueness of Solutions for a Third‐Order Three‐Point Boundary Value Problem via Measure of Noncompactness

“…In this paper, we study the nonlinear third-order three-point boundary value problem (6). First, we construct Green's function for the third-order three-point boundary value problem (22) and discuss its properties. Second, based on Green's function and its properties, we define a solution operator H. en, we prove that H has at least a fixed point by using Darbo's fixed point theorem combined with the technique of measure of noncompactness.…”

“…A new direction of research with the presentation of the notion of a measure of noncompactness was opened up in 1930 by Kuratowski, which can be applied to prove the existence results related to various integral, differential equations, integro-differential equations as well as their systems. As an important application of this measure, Darbo's fixed point theorem generalizes the Schauder-fixed point theorem and Banach contraction principle, especially in proving the existence of solutions for classes of nonlinear equations (see [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]).…”

Extension of Darbo’s fixed point theorem via shifting distance functions and its application

“…Namely, a fixed positive nonincreasing real sequence α = (α σ ) ∞ σ=1 is called a tempering sequence. Recently, Rabbani et al [26] denoted by W a collection of all real or complex se-…”

“…Different real-life situations, which are modeled via FIEs, can be studied using FPT and measure of noncompactness (MNC) (see [2,3,5,7,10,11,13,19,21,[23][24][25][26]).…”

Existence of solutions for an infinite system of tempered fractional order boundary value problems in the spaces of tempered sequences

“…Fractional differential equations with boundary conditions have occupied an important area in the fractional calculus domain, since these problems appear in various applications of sciences and engineering: mechanics, finance, control theory, electricity, chemistry, biology, chemistry, economics [8,10,32,35,36]. The progress of this field has motivated researchers to investigate in some interesting questions related to existence, uniqueness and stability of solutions [13,23,[25][26][27]31].…”