Some new uniqueness and Ulam–Hyers type stability results for nonlinear fractional neutral hybrid differential equations with time-varying lags
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Nguyen Minh Dien
Abstract
This paper deals with some qualitative properties of solutions to nonlinear neutral hybrid differential equations connected to ψ-Caputo fractional derivative with time-varying lags. First, we demonstrate the problem possesses a mild solution uniquely where the source function may have temporal singularities. Second, in some cases, we indicate that the problem possesses a unique mild solution under some weaker conditions than the previous one. Third, we also obtain a result on a global mild solution for the problem. Finally, the results are further enriched by studying a new type of Ulam–Hyers stability for the main equation. The main results are obtained by applying the nice inequality, first proposed and proven in this paper. Some befit examples are given to justify the applicability of the main results.
Acknowledgement
The author heartily expresses his gratitude to the handing editor and the anonymous reviewers for suggestions that improved the manuscript.
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Communicated by Michal Fečkan
References
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Articles in the same Issue
- Right algebras in Sup and the topological representation of semi-unital and semi-integral quantales, revisited
- Topological representation of some lattices
- Exact-m-majority terms
- Polynomials whose coefficients are generalized Leonardo numbers
- A study on error bounds for Newton-type inequalities in conformable fractional integrals
- Improved conditions for the distributivity of the product for σ-algebras with respect to the intersection
- Close-to-convex functions associated with a rational function
- Complete monotonicity for a ratio of finitely many gamma functions
- Class of bounds of the generalized Volterra functions
- Some new uniqueness and Ulam–Hyers type stability results for nonlinear fractional neutral hybrid differential equations with time-varying lags
- Existence of positive solutions to a class of boundary value problems with derivative dependence on the half-line
- Solving Fredholm integro-differential equations involving integral condition: A new numerical method
- Bounds of some divergence measures on time scales via Abel–Gontscharoff interpolation
- Weighted 1MP and MP1 inverses for operators
- Non-commutative effect algebras, L-algebras, and local duality
- Operator Bohr-type inequalities
- Some results for weighted Bergman space operators via Berezin symbols
- Lower separation axioms in bitopogenous spaces
- Fisher information in order statistics and their concomitants for Cambanis bivariate distribution
- Irreducibility of strong size levels