Extension of Colombeau algebra to derivatives of arbitrary order , . Application to ODEs and PDEs with entire and fractional derivatives

✍ Scribed by Mirjana Stojanović

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 936 KB
• Volume: 71
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2009.04.034

✦ Synopsis

Extension of Colombeau algebra to derivatives of arbitrary order D α , α ∈ R + ∪ {0} Fractional derivatives Applications to ODEs and PDEs ODEs and PDEs driven by fractional derivatives of delta distribution a b s t r a c t

We give an extension of Colombeau algebra of generalized functions to fractional derivatives. We apply it in solving ODEs and PDEs with entire and fractional derivatives with respect to temporal and spatial variables. We give applications to ODEs and PDEs driven by fractional derivatives of delta distribution.