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We prove a new Taylor’s theorem for generalized weighted fractional calculus with nonsingular kernels. The proof is based on the establishment of new relations for nth-weighted generalized fractional integrals and… Click to show full abstract
We prove a new Taylor’s theorem for generalized weighted fractional calculus with nonsingular kernels. The proof is based on the establishment of new relations for nth-weighted generalized fractional integrals and derivatives. As an application, new mean value theorems for generalized weighted fractional operators are obtained. Direct corollaries allow one to obtain the recent Taylor’s and mean value theorems for Caputo–Fabrizio, Atangana–Baleanu–Caputo (ABC) and weighted ABC derivatives.
Keywords:
taylor formula;
weighted fractional;
nonsingular kernels;
formula generalized;
fractional derivatives;
generalized weighted
Journal Title: Axioms
Year Published: 2022
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Journal Title: Axioms
Year Published: 2022
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!