A NEW EXISTENCE RESULT OF UNIQUE SOLUTION FOR CLASS OF FRACTIONAL DIFFERENTIAL EQUATIONS INVOLVING SEQUENTIAL OPERATORS AND NONLINEAR PERTURBATIONS IN WEIGHTED SOBOLEV SPACES
Keywords:
Riemann–Liouville fractional differential equation, non-local conditions, weighted Sobolev spaces, fixed point theorem, Mittag-Leffler function, fractional derivatives. AMS Classification: 34A08; 34A34; 34L30Abstract
In this work, we investigated a class of fractional differential boundary value prob lems characterized by sequential operators and nonlinear perturbations. By converting the original system into an equivalent integral formulation, we can apply Banach’s fixed point theorem to study the existence of a unique solution to the system under appropriate assumptions on the nonlinearities. The results presented here not only unify several previ ously known results but also extend them to a broader class of fractional systems involving sequential operators.
