On the Ulam–Hyers–Rassias stability for nonlinear fractional differential equations using the $$\psi $$ψ-Hilfer operator

By J. Sousa, E. Capelas de Oliveira. Journal of Fixed Point Theory and Applications, 2017

165 citations recorded by the source corpus.

We study the existence and uniqueness of solution of a nonlinear Cauchy problem involving the $$\psi $$ψ-Hilfer fractional derivative. In addition, we discuss the Ulam–Hyers and Ulam–Hyers–Rassias stabilities of its solutions. A few examples are presented to illustrate the possible applications of our main results.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/72330649d5a0405b5fbc6e488e61682c8e5e238b

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In Applied Mathematics

1. Ashwini D. Mali
2. Kamal Shah
3. Poom Kumam
4. Kishor D. Kucche

In Modeling and Simulation

1. Ashwini D. Mali
2. Kamal Shah
3. Kishor D. Kucche

Citations in the corpus

• Nonlocal boundary value problem for generalized Hilfer implicit fractional differential equations (2020, background): “The implicit FDEs involving φ-Hilfer derivative has been investigated in [30] for the existence and uniqueness of the solution and the Ulam-Hyers-Rassias stability.”
• Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition (2020, background): “Motivated by the papers [21,47,48] and some familiar results on fractional pantograph differential equations [16,52,55,58].”