Existence and uniqueness for a problem involving Hilfer fractional derivative

By Khaled M. Furati, Mohammed D. Kassim, Nasser-Eddine Tatar. Computers and Mathematics with Applications, 2012

530 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/aca2444c5db462cdf21595f4fd56050bfd8da740

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In Applied Mathematics

In Modeling and Simulation

Citations in the corpus

Nonlocal boundary value problem for generalized Hilfer implicit fractional differential equations (2020, unknown): “Equation (1) is generalized Ulam–Hyers–Rassias stable, with respect to the χ ∈ C( J, R+), if there exists a Cf,χ > 0 such that for each solution z ∈ C2−ξ; Ψ ( J,R) of the inequality |||Hμ, ν ; Ψ a+ z(t) − f (t, z(t), Hμ, ν ; Ψ a+ z(t))||| ≤ χ(t), t ∈ J, (39) there exists solution y ∈ C2−ξ; Ψ ( J,R”
Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition (2020, methodology): “[5] proposed a Hilfer fractional derivatives which interpolates with Riemann-Liouville and Caputo fractional derivatives.”
Existence results of Hilfer integro-differential equations with fractional order (2020, methodology): “The couple of parameter family of fractional derivative with ζ, η permits one to interpolate between the R-L and the Caputo derivative discussed in Hilfer [8, 10, 11, 22, 31] fractional derivative.”
Stability of the fractional Volterra integro‐differential equation by means of ψ‐Hilfer operator (2018, background): “We also mention some recent papers by Katugampola,5 Almeida,6 and Sousa and Oliveira.7,8 Fractional differential equations have already proved to be valuable tools in the modeling of several physical phenomena, because their solutions, in general, allows a better evaluation of the results in several”
On the Ulam–Hyers–Rassias stability for nonlinear fractional differential equations using the $$\psi $$ψ-Hilfer operator (2017, unknown): “H D α,β;ψ a+ y (t) = H D α,β;ψ a+ (ψ (t) − ψ (a))γ−1 Γ (γ) ya + D α,β;ψ a+ I α;ψ a+ g (t) = g (t) , where, for 0 < γ < 1, we have HD a+ (ψ (t) − ψ (a))γ−1 = 0 [2,10].”
Some Existence and Stability Results for Hilfer-fractional Implicit Differential Equations with Nonlocal Conditions (2018, unknown): “The following observations are taken from [12,13, 15,16,28].”