Variable Order Mittag–Leffler Fractional Operators on Isolated Time Scales and Application to the Calculus of Variations

2018/09/06 by Thabet Abdeljawad, Raziye Mert, Delfim F. M. Torres
Mathematics · #Approximation Theory and Sequence Spaces #Calculus (dental) #Calculus of variations #Class (philosophy) #Fractional Differential Equations Solutions #Fractional calculus #Nonlinear Differential Equations Analysis #Operator theory #Order (exchange) #Time-scale calculus #Variable (mathematics) #math.CA #math.OC #msc:26A33 #msc:26E70 #msc:49K05

paper · pdf · doi:10.1007/978-3-030-11662-0_3

published as Studies in Systems, Decision and Control 194 (2019), 35--47 · This is a preprint of a paper whose final and definite form is with Springer

arxiv created 2018/09/06 · openalex created_date 2018/09/27 · openalex publication_date 2019/01/01 · arxiv updated 2019/02/19 · openalex updated_date 2026/08/05

Abstract

We introduce new fractional operators of variable order on isolated time scales with Mittag-Leffler kernels. This allows a general formulation of a class of fractional variational problems involving variable-order difference operators. Main results give fractional integration by parts formulas and necessary optimality conditions of Euler-Lagrange type.

Citations

• Fractional Herglotz variational problems of variable order
• Combined fractional variational problems of variable order and some computational aspects
• Applications of New Time and Spatial Fractional Derivatives with Exponential Kernels
• New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model