On the boundary value problems of Hadamard fractional differential equations of variable order
Amar Benkerrouche, Mohammed Said Souıd, Erdal Karapınar, Ali Hakem
Abstract
In this manuscript, we examine both the existence, uniqueness, and the stability of solutions to the boundary value problem (BVP) of Hadamard fractional differential equations of variable order by converting it into an equivalent standard Hadamard (BVP) of the fractional constant order with the help of the generalized intervals and the piecewise constant functions. All results in this study are established using Krasnoselskii fixed‐point theorem and the Banach contraction principle. Further, the Ulam–Hyers stability of the given problem is examined, and finally, we construct an example to illustrate the validity of the observed results.
Topics & Concepts
MathematicsHadamard transformUniquenessPiecewiseMathematical analysisBoundary value problemFixed-point theoremConstant (computer programming)Contraction principleVariable (mathematics)Applied mathematicsBanach fixed-point theoremConstant coefficientsOrder (exchange)Differential equationFractional calculusComputer scienceEconomicsFinanceProgramming languageFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Numerical Methods