A New Definition of Fractional Derivatives With Mittag-Leffler Kernel of Two Parameters

Sanjay Madhukar Chinchole; Ashok Bhadane

doi:10.26713/cma.v13i1.1689

Authors

Sanjay Madhukar Chinchole Department of Mathematics, Mahatma Gandhi Vidyamandir’s Arts, Science and Commerce College (Savitribai Phule Pune University), Manmad 423104, India https://orcid.org/0000-0003-1670-4814 (unauthenticated)
Ashok Bhadane Department of Mathematics, L. V. H. Mahavidyalaya (Savitribai Phule Pune University), Panchavati, Nashik 422003, India https://orcid.org/0000-0002-6359-7575 (unauthenticated)

DOI:

https://doi.org/10.26713/cma.v13i1.1689

Keywords:

fractional derivatives, non-local kernel, non-singular kernel, Mittag-Leffler function of two parameters, fractional time Fourier's law equation

Abstract

In this paper, a new fractional derivative with Mittag-Leffler kernel of two parameters is proposed. Several functional properties of this derivative are explained and applied to solve the fractional time Fourier’s law equation.

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