Fractional Cauchy problems associated with the bi-ordinal Hilfer fractional q-derivative

2022/12/14 by Karimov, Erkinjon, Ruzhansky, Michael, Shaimardan, Serikbol
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2212.07374

Abstract

To study the existence and uniqueness of solutions to Cauchy-type problems for fractional q-difference equations with the bi-ordinal Hilfer fractional q-derivative which is an extension of the Hilfer fractional q-derivative. An approach is based on the equivalence of the nonlinear Cauchy-type problem with a nonlinear Volterra q-integral equation of the second kind. Applying an analog of Banach fixed point theorem we prove the uniqueness and the existence of the solution. Moreover, we present an explicit solution to the q-analog of the Cauchy problem for the linear case.

Related

• Existence and uniqueness of some Cauchy Type Problems in fractional q-difference calculus
• Hilfer-Hadamard-Type Fractional Differential Equation with Cauchy-Type Problem
• Existence and uniqueness of solution of Cauchy-type problem for Hilfer fractional differential equations
• Study of new class of q-fractional derivative and its properties
• Non-local boundary value problem for a mixed-type equation involving the bi-ordinal Hilfer fractional differential operators