Solvability of ψ-Hilfer Fractional Differential Equations in the Space of Summable Functions

Montalvo Bonilla M.; Vera Baca J.; Torres Ledesma C.E. · Mediterranean Journal of Mathematics (2024) · DOI: 10.1007/s00009-024-02753-7

Resumen

This paper is devoted to study the Cauchy type problem for the nonlinear differential equation with ψ-Hilfer fractional derivative (Formula presented.) in the space of summable functions Lα,ν[a,b], where α∈(0,1), ν∈(0,1), ψ∈C1[a,b] be a strictly increasing function and HDaα,ν;ψ is the ψ-Hilfer fractional derivative of u. The equivalence of this problem and the nonlinear Volterra integral equation is established. The existence and uniqueness of solution to the Cauchy type problem is proved using progressive contractions techniques and the Banach fixed point theorem. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.

Instituciones: Universidad Nacional de Trujillo