On Multi-Order Fractional Differential Operators in the Unit Disk

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Ibrahim R. W., Ozel C.

FILOMAT, vol.30, no.1, pp.73-81, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 1
  • Publication Date: 2016
  • Doi Number: 10.2298/fil1601073i
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.73-81
  • Keywords: analytic function, fractional calculus, fractional differential equation, unit disk, ANALYTIC-FUNCTIONS, OPTICAL PATHLENGTH, EXTINCTION
  • Dokuz Eylül University Affiliated: No

Abstract

In this article, we generalize fractional operators (differential and integral) in the unit disk. These operators are generalized the Srivastava-Owa operators. Geometric properties are studied and the advantages of these operators are discussed. As an application, we impose a method, involving a memory formalism of the Beer-Lambert equation based on a new generalized fractional differential operator. We give solutions in terms of the multi-index Mittag-Leffler function. In addition, we sanctify the out come from a stochastic standpoint. We utilize the generalized Wright function to obtain the analytic formula of solutions.