Filomat 2023 Volume 37, Issue 20, Pages: 6891-6903
https://doi.org/10.2298/FIL2320891H
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Existence and Mittag-Leffler-Ulam-Stability results of sequential fractional hybrid pantograph equations
Houas Mohamed (Laboratory FIMA, UDBKM, Khemis Miliana university, Algeria), m.houas.st@univ-dbkm.dz
Abbas Mohamed I. (Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt), miabbas@alexu.edu.eg
Martínez Francisco (Department of Applied Mathematics and Statistics, Technological University of Cartagena, Cartagena, Spain), f.martinez@upct.es
In this present work, the existence and uniqueness of solutions for
fractional pantograph differential equations involving Riemann-Liouville and
Caputo fractional derivatives are established by applying contraction
mapping principle and Leray-Schauder’s alternative. The Mittag-Leffler-Ulam
stability results are also obtained via generalized singular Gronwall’s
inequality. Finally, we give an illustrative example.
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