Fractional Integro-Differential Equations Involving $\psi$-Hilfer Fractional Derivative
By Mohammed S. Abdo and Satish K. Panchal. Advances in Applied Mathematics and Mechanics, 2019
78 citations recorded by the source corpus.
Considering a fractional integro-differential equation involving a general form of Hilfer fractional derivative with respect to another function. We show that weighted Cauchy-type problem is equivalent to a Volterra integral equation, we also prove the existence, uniqueness of solutions and Ulam-Hyers stability of this problem by employing a variety of tools of fractional calculus including Banach fixed point theorem. An example is provided to illustrate our main results. AMS subject classifications: 34K37, 26A33, 34A12, 47H10
Subfields: Applied Mathematics, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/5dc0102b15b7e3fe54ec6ed9150606cbcb50ab8f
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In Applied Mathematics
In Modeling and Simulation
Citations in the corpus
- On the existence of positive solutions for generalized fractional boundary value problems (2019, unknown): “In [1], Abdo and Panchal considered a general form of ψ-Hilfer fractional derivative with respect to another function of a fractional integro-differential equation.”
- 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].”