Abstract
This article is dedicated to the existence results of solutions for boundary value problems of inclusion type. We suggest the infinite countable system to fractional differential inclusions written byDαABCνit∈Yit,νiti=1∞. The mappingsyit,νiti=1∞are proposed to be Lipschitz multivalued mappings. The results are explored according to boundary conditionσνi0=γνiρ, σ,γ∈ℝ. This type of condition is the generalization of periodic, almost, and antiperiodic types.
Highlights
Consider the following infinite system: ABCDα]i(t) ∈ yit, ]j (t)∞ j 1, i ∈ N, t ∈ [0, ρ], (1)σ]i(0) c]i(ρ), σ, c ∈ R, (2)where ABCDα denotes the Atangana–Baleanu fractional derivative in the Caputo sense of order α ∈ (0, 1] and yii∈N is an infinite countable family of Lipschitz continuous multivalued mappings. is means there is an infinite countable sequence of continuous real-valued functions]i(t)i∈N satisfying define the function problems (1) and (2)
We suggest the infinite countable system to fractional differential inclusions written by ABCDα[]i(t)] ∈ Yi(t, ]i(t)∞ i 1). e mappings yi(t, ]i(t)∞ i 1) are proposed to be Lipschitz multivalued mappings. e results are explored according to boundary condition σ]i(0) c]i(ρ), σ, c ∈ R. is type of condition is the generalization of periodic, almost, and antiperiodic types
In [19], we studied how to generate the differential equations and inclusions by one form. en, we studied the solvability of this form
Summary
Where ABCDα denotes the Atangana–Baleanu fractional derivative in the Caputo sense of order α ∈ In the field of infinite systems, the research to fractional differential problems started via ordinary derivatives (see [1,2,3,4] and the mentioned references therein). E fractional differential operators are capable of capturing the behavior of multifaceted media as they have diffusion processes In this field, many researchers have paid attention in several ways to develop these derivatives. In [20], we generated the fractional differential equation at resonance on the half line into the inclusion one and explored the existence results of positive solutions for this problem. It is worth remarkable to mention that the field of studying the existence and uniqueness of solutions to fractional differential equations has drawn attention of many contributors [21,22,23,24,25,26,27,28]
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