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

2014/11/07 by Udita N. Katugampola, Katugampola, Udita N. · 2 citations
Mathematics · #26A33 #34A08 #34A12 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #math.CA #msc:26A33 #msc:34A08 #msc:34A12

paper · pdf · doi:10.48550/arxiv.1411.5229

9 pages, submitted for publication

openalex publication_date 2014/11/07 · arxiv created 2016/06/09 · arxiv updated 2016/06/13 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

The author (Bull. Math. Anal. App. 6(4)(2014):1-15), introduced a new fractional derivative, ^ρD_a^αf (x) = \fracρ^α-n+1Γ(n-α) (x^1-ρ (d)/(dx))ⁿ ∫^x_a \fracτ^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.

Citations

• Fractional calculus - A different approach to the analysis of viscoelastically damped structures
• Fractional Differential Equations

Cited by

• Theory of Nonlinear Caputo-Katugampola Fractional Differential Equations
• Non-existence of Global Solutions for a Generalized Fractional Differential Problem

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