Analog of the Darboux problem for a loaded integro-differential equation involving the Caputo fractional derivative
Umida Baltaeva, Yolqin Alikulov, Iroda Ismailovna Baltaeva, A.I. Ashirova
Abstract
In this paper, we prove the unique solvability of an analogue problem Darboux for a loaded integro-differential equation with Caputo operator by method of integral equations. The problem is equivalently reduced to a system of integral equations, which is unconditionally and uniquely solvable.
Topics & Concepts
Integro-differential equationFractional calculusDerivative (finance)MathematicsDifferential equationDifferential (mechanical device)Applied mathematicsMathematical analysisPhysicsRiccati equationThermodynamicsFinancial economicsEconomicsDifferential Equations and Boundary ProblemsDifferential Equations and Numerical MethodsNonlinear Differential Equations Analysis