Browsing by Subject "integro-differential equation"

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Access status: Open Access ,
Existence of minimal and maximal solutions to RL fractional integro-differential initial value problems
(Wydawnictwa AGH, 2017) Denton Zachary; Ramírez, J.D.
In this work we investigate integro-differential initial value problems with Riemann Liouville fractional derivatives where the forcing function is a sum of an increasing function and a decreasing function. We will apply the method of lower and upper solutions and develop two monotone iterative techniques by constructing two sequences that converge uniformly and monotonically to minimal and maximal solutions. In the first theorem we will construct two natural sequences and in the second theorem we will construct two intertwined sequences. Finally, we illustrate our results with an example.
Access status: Open Access ,
On the summability of divergent power series solutions for certain first-order linear PDES
(2015) Hibino, Masaki
This article is concerned with the study of the Borel summability of divergent power series solutions for certain singular first-order linear partial differential equations of nilpotent type. Our main purpose is to obtain conditions which coefficients of equations should satisfy in order to ensure the Borel summability of divergent solutions. We will see that there is a close affinity between the Borel summability of divergent solutions and global analytic continuation properties for coefficients of equations.