Fixed Point and Endpoint Theories for Two Hybrid Fractional Differential Inclusions with Operators Depending on an Increasing Function

The main concentration of the present research is to explore several theoretical criteria for proving the existence results for the suggested boundary problem. In fact, for the first time, we formulate a new hybrid fractional differential inclusion in the φ -Caputo settings depending on an increasing function φ subject to separated mixed φ -hybrid-integro-derivative boundary conditions. In addition to this, we discuss a special case of the proposed φ -inclusion problem in the non- φ -hybrid structure with the help of the endpoint notion. To confirm the consistency of our findings, two specific numerical examples are provided which simulate both φ -hybrid and non- φ -hybrid cases.

On Caputo–Hadamard type coupled systems of nonconvex fractional differential inclusions

This research article is mainly concerned with the existence of solutions for a coupled Caputo–Hadamard of nonconvex fractional differential inclusions equipped with boundary conditions. We derive our main result by applying Mizoguchi–Takahashi’s fixed point theorem with the help of $\mathcal{P}$ P -function characterizations.

Impulsive Fractional Differential Inclusions and Almost Periodic Waves

In the present paper, the concept of almost periodic waves is introduced to discontinuous impulsive fractional inclusions involving Caputo fractional derivative. New results on the existence and uniqueness are established by using the theory of operator semigroups, Hausdorff measure of noncompactness, fixed point theorems and fractional calculus techniques. Applications to a class of fractional-order impulsive gene regulatory network (GRN) models are proposed to illustrate the results.

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

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 by D α ABC ν i t ∈ Y i t , ν i t i = 1 ∞ . The mappings y i t , ν i t i = 1 ∞ are proposed to be Lipschitz multivalued mappings. The results are explored according to boundary condition σ ν i 0 = γ ν i ρ , σ , γ ∈ ℝ . This type of condition is the generalization of periodic, almost, and antiperiodic types.