On a new structure of the pantograph inclusion problem in the Caputo conformable setting

• Published in: Boundary value problems Vol. 2020; no. 1; pp. 1 - 21
• Main Authors: Thabet, Sabri T. M., Etemad, Sina, Rezapour, Shahram
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 11.11.2020; Hindawi Limited; SpringerOpen
• Subjects: Analysis; Approximations and Expansions; Difference and Functional Equations; Differential equations; Inclusion problem; Mathematics; Mathematics and Statistics; Operators (mathematics); Ordinary Differential Equations; Pantograph differential equation; Pantographs; Partial Differential Equations; The Caputo conformable derivative; The lower and upper semi-continuity; The lower and upper semi-continuity; Inclusion problem; 34A12; Pantograph differential equation; The Caputo conformable derivative; 34A08
• ISSN: 1687-2770; 1687-2762; 1687-2770
• DOI: 10.1186/s13661-020-01468-4

In this work, we reformulate and investigate the well-known pantograph differential equation by applying newly-defined conformable operators in both Caputo and Riemann–Liouville settings simultaneously for the first time. In fact, we derive the required existence criteria of solutions corresponding...