Tripled Fixed Points and Existence Study to a Tripled Impulsive Fractional Differential System via Measures of Noncompactness

Abstract

In this paper, a tripled fractional differential system is introduced as three associated impulsive equations. The existence investigation of the solution is based on contraction principle and measures of noncompactness in terms of tripled fixed point and modulus of continuity. Our results are valid for both Kuratowski and Hausdorff measures of noncompactness. As an application, we apply the obtained results to a control problem.

Theory of Fractional Hybrid Problems in the Frame of ψ -Hilfer Fractional Operators

“…So, we are sure that the obtained results will be a beneficial contribution and an extension of the current results in the literature. We will also refer here to some recent results related to the subject of our study (see [25][26][27][28][29][30][31]).…”

“…Let ϰ ∈ C 1−θ,ψ ðI, ℝÞ be a solution of (29). We need to prove that ϰ is also a solution of (30). By the definition of C 1−θ,ψ ðI, ℝÞ and Lemma 6, we have I 1−θ;ψ a + ϰðϑÞ ∈ CðI, ℝÞ:…”

Chebyshev-Type Inequalities Involving ( k , ψ )-Proportional Fractional Integral Operators

“…In [10], authors studied Pólya-Szegö-type inequalities and Grüss-type inequalities with the help of ðk, ψÞ-proportional fractional operators. In recent years, many researchers have been working in the direction of estimating the fractional version of various inequalities [13][14][15][16][17][18][19] and the references given there.…”

Existence Results for Impulsive Fractional Integrodifferential Equations Involving Integral Boundary Conditions

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