Existence and Uniqueness results for a class of Generalized Fractional Differential Equations

Abstract

The author (Bull. Math. Anal. App. 6(4)(2014):1-15), introduced a new fractional derivative, \[{}^ρ\mathcal{D}_a^αf (x) = \frac{ρ^{α-n+1}}{Γ({n-α})} \, \bigg(x^{1-ρ} \,\frac{d}{dx}\bigg)^n \int^x_a \frac{τ^{ρ-1} f(τ)}{(x^ρ- τ^ρ)^{α-n+1}}\, dτ\] which generalizes two familiar fractional derivatives, namely, the Riemann-Liouville and the Hadamard fractional derivatives to a single form. In this paper, we derive the existence and uniqueness results for a generalized fractional differential equation governed by the fractional derivative in question.

9 pages, submitted for publication

References in corpus (6)

• New Approach To A Generalized Fractional Integral
• A New Approach to Generalized Fractional Derivatives
• Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative
• Mellin Transforms of the Generalized Fractional Integrals and Derivatives
• A Generalized Fractional Calculus of Variations
• An approximation formula for the Katugampola integral

Cited by in corpus (6)

• Hermite-Hadamard and Hermite-Hadamard-Fejér type Inequalities for Generalized Fractional Integrals
• New fractional integral unifying six existing fractional integrals
• Fractional differential equations with dependence on the Caputo-Katugampola derivative
• Existence and Stability of Fractional Differential Equations Involving Generalized Katugampola Derivative
• Theory of Nonlinear Caputo-Katugampola Fractional Differential Equations
• Non-existence of Global Solutions for a Generalized Fractional Differential Problem