Caputo q-Fractional Initial Value Problems and a q-Analogue Mittag-Leffler Function

Abstract

Caputo q-fractional derivatives are introduced and studied. A Caputo -type q-fractional initial value problem is solved and its solution is expressed by means of a new introduced q-Mittag-Leffler function. Some open problems about q-fractional integrals are proposed as well.

References in corpus (1)

• Discrete-Time Fractional Variational Problems

Cited by in corpus (4)

• Generalized Fractional Operators on Time Scales with Application to Dynamic Equations
• A difference method for solving the nonlinear $q$-factional differential equations on time scale
• A monotonicity result for the $q-$fractional operator
• A Quantum Generalized Mittag-Leffler Function Via Caputo q-Fractional Equations