Fractional integro-differential equations with dual anti-periodic boundary conditions
Bashir Ahmad, Ymnah Alruwaily, Ahmed Alsaedi, Juan J. Nieto
Abstract
In this paper, we introduce a new concept of dual anti-periodic boundary conditions. One of these conditions relates to the end points of an interval of arbitrary length, while the second one involves two nonlocal positions within the interval. Equipped with these conditions, we present the criteria for the existence of solutions for a fractional integro-differential equation involving two Caputo fractional derivatives of different orders and a Riemann-Liouville integral. Our study relies on the modern methods of functional analysis. Examples are constructed for illustrating the obtained results.
Topics & Concepts
MathematicsInterval (graph theory)Dual (grammatical number)Mathematical analysisBoundary value problemDifferential equationFractional calculusApplied mathematicsCombinatoricsLiteratureArtNonlinear Differential Equations AnalysisDifferential Equations and Boundary ProblemsFractional Differential Equations Solutions