Some Existence and Stability Results for Hilfer-fractional Implicit Differential Equations with Nonlocal Conditions

By D. Vivek, K. Kanagarajan, Elsayed M. Elsayed. Mediterranean Journal of Mathematics, 2018

103 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/7f0dc399b4d85f79423f766a8ead7c4d5c730e9d

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In Applied Mathematics

In Modeling and Simulation

Citations in the corpus

Stability of the fractional Volterra integro‐differential equation by means of ψ‐Hilfer operator (2018, background): “Also, several investigators used the fractional derivatives and studied the stability of Ulam-Hyers and Ulam-Hyers-Rassias [27, 28, 29].”
Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition (2020, background): “In [48], the authors considered an implicit fractional differential equations with nonlocal condition described by: { D 0+ w(τ) = f (τ, w(τ), D α,β 0+ w(τ)), τ ∈ I = [0, T], I1−γ 0+ w(0) = ∑ m i=1 ciw(ηi), α ≤ γ = α + β− αβ, ηi ∈ [0, T], (2)”
Nonlocal boundary value problem for generalized Hilfer implicit fractional differential equations (2020, unknown): “Using Equations (43) and (47), we have |z(t) − 𝑦(t)| = |||||z(t) − [ (𝛹 (t) − 𝛹 (a))𝜉−1Ã𝑦 + 1 Γ(𝜇) ∫ t a 𝛹 ′(s)(𝛹 (t) − 𝛹 (s))𝜇−1g𝑦(s)ds ]||||| ≤ |||||z(t) − (𝛹 (t) − 𝛹 (a))𝜉−1Ãz − 1Γ(𝜇) ∫ t a 𝛹 ′(s)(𝛹 (t) − 𝛹 (s))𝜇−1gz(s)ds ||||| + ||||| 1Γ(𝜇) ∫ t a 𝛹 ′(s)(𝛹 (t) − 𝛹 (s))𝜇−1g”
On the Ulam–Hyers–Rassias stability for nonlinear fractional differential equations using the $$\psi $$ψ-Hilfer operator (2017, background): “Furthermore, for other examples of implicit fractional differential equations, we suggest [27,28,32,34,35].”