Existence theorems and Hyers-Ulam stability for a class of Hybrid fractional differential equations with $p$-Laplacian operator

By Hasib Khan, Cemil Tunç, Wen Chen, Aziz Khan. 2018

89 citations recorded by the source corpus.

In this paper, we prove necessary conditions for existence and uniqueness of solution (EUS) as well Hyers-Ulam stability for a class of hybrid fractional differential equations (HFDEs) with p-Laplacian operator. For these aims, we take help from topological degree theory and Leray Schauder-type fixed point theorem. An example is provided to illustrate the results.

Subfields: Applied Mathematics, Geometry and Topology, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/16d5aa4a4fb51c057b059e46f24a172e896c820a

Citations in the corpus

• Existence of solution for a fractional‐order Lotka‐Volterra reaction‐diffusion model with Mittag‐Leffler kernel (2019, unknown): “Then the fractional-order L-V in ABC difference form (6) has a unique solution provided that the following holds true: [ 1 − α1 (α1) + 1 (α1)Γ(α1) ] (d1λ1 + r ∗ 1 + r ∗ 1 a ∗ 11η1 + r ∗ 1 a ∗ 12δ2 + r ∗ 1 a ∗ 13δ3) ≤ 1, (37) [ 1 − α2 (α2) + 1 (α2)Γ(α2) ] (d2λ2 + r ∗ 2 + r ∗ 2 a ∗ 21δ1 + r ∗ 2 a ”