Existence of solution of an infinite system of generalized fractional differential equations by Darbo’s fixed point theorem

Measure of noncompactness for an infinite system of fractional Langevin equation in a sequence space

“…where ρ = 9 10 , λ i = 3 2 , μ i = 3 4 , ν i = 1 8 , ξ i = 10 -i , a i = 1, η i = 1 6 , and φ i (x) = 1 5 x. Also, we take…”

“…Recently, Seemab and Rehman [9] investigated the fractional infinite system ρ c D α u i (t) = f i t, u(t), ψ ρ c D β u(t) , t ∈ (0, 1) in the Banach space c 0 , where u(t) = {u i (t)} ∞ i=1 and ψ : c 0 → c 0 is a continuous linear function such that ψ(0) = 0, with the initial conditions…”

Compact and Noncompact Solutions to Generalized Sturm–Liouville and Langevin Equation with Caputo–Hadamard Fractional Derivative

“…e underlying idea is there are two measures of noncompactness commonly used; these associate numbers to sets in such a way that compact sets all get the measure 0, and other sets get measures that are bigger according to "how far" they are removed from compactness. ere are many contributors who used measure of noncompactness to investigate the existence of solution to FoDE [32][33][34] and references given therein. e remaining of this paper is ordered as follows: Section 2 presents briefly some fundamental concepts related to the fractional calculus and fixed point theorems.…”

A Countable System of Fractional Inclusions with Periodic, Almost, and Antiperiodic Boundary Conditions

“…en, many scholars were attracted to develop these problems into the ones associated with fractional derivatives. For instance, see the required results in [5][6][7][8] and references cited therein. e importance of the infinite system was arising naturally in the description of physical problems such as stochastic (stochastic metapopulation) models [9,10], models descried by the Becker-Döring cluster [11,12], and optimal pursuit equations [13] and the control problems for the models descried by parabolic and hyperbolic equations [14].…”