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Lachachi-Merad, Nardjis; Baghli-Bendimerad, Selma; Benchohra, Mouffak

Unique mild solution for Caputo’s fractional perturbed evolution equations with state-dependent delay. (English) Zbl 1530.34065

Evol. Equ. Control Theory 13, No. 1, 160-172 (2024).
Summary: This study examines if there are any mild solutions for the perturbed partial functional and neutral functional evolution equations with state-dependent delay when the derivative utilizes Caputo’s fractional derivative, as well as whether any such solutions are unique. The solution itself determines how long the equations take to solve. The work proves the existence and uniqueness of these solutions using semigroup theory and the Banach contraction theorem in Banach spaces.

MSC:

34K37 Functional-differential equations with fractional derivatives
34K40 Neutral functional-differential equations
37L05 General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations
34G20 Nonlinear differential equations in abstract spaces

Keywords:

perturbed evolution equations; neutral problems; Caputo’s fractional derivative; existence of solution; uniqueness; state-dependent delay; nonlinear alternative; fixed point; semigroup theory
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References:

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