On the impulsive implicit Ψ‐Hilfer fractional differential equations with delay
Copyright policy )On the impulsive implicit Ψ‐Hilfer fractional differential equations with delay
In this paper, we investigate the existence and uniqueness of solutions and derive the Ulam‐Hyers‐Mittag‐Leffler stability results for impulsive implicit Ψ‐Hilfer fractional differential equations with time delay. It is demonstrated that the Ulam‐Hyers and generalized Ulam‐Hyers stability are the specific cases of Ulam‐Hyers‐Mittag‐Leffler stability. Extended version of the Gronwall inequality, abstract Gronwall lemma, and Picard operator theory are the primary devices in our investigation. We provide an example to illustrate the obtained results.
- Shivaji University India
Perturbations of functional-differential equations, Stability theory of functional-differential equations, \( \Psi \)-Hilfer derivative, Inequalities involving derivatives and differential and integral operators, Functional-differential equations with impulses, fractional differential equations, Dynamical Systems (math.DS), fractional integral inequality, stability, Mathematics - Analysis of PDEs, FOS: Mathematics, Mathematics - Dynamical Systems, Implicit functional-differential equations, Functional-differential equations with fractional derivatives, existence and uniqueness, Analysis of PDEs (math.AP)
Perturbations of functional-differential equations, Stability theory of functional-differential equations, \( \Psi \)-Hilfer derivative, Inequalities involving derivatives and differential and integral operators, Functional-differential equations with impulses, fractional differential equations, Dynamical Systems (math.DS), fractional integral inequality, stability, Mathematics - Analysis of PDEs, FOS: Mathematics, Mathematics - Dynamical Systems, Implicit functional-differential equations, Functional-differential equations with fractional derivatives, existence and uniqueness, Analysis of PDEs (math.AP)
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