On the Generalization of κ-Fractional Hilfer-Katugampola Derivative with Cauchy Problem

DOI10.3906/mat-2007-67zbMath1506.26006OpenAlexW3124103822MaRDI QIDQ5100190

Samaira Naz, Muhammad Nawaz Naeem

Publication date: 29 August 2022

Published in: TURKISH JOURNAL OF MATHEMATICS (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3906/mat-2007-67

zbMATH Keywords

\(\kappa\)-gamma function\(\kappa\)-Mittag-Leffler function\(\kappa\)-Riemann-Liouville fractional integralgeneralized \(\kappa\)-fractional derivative

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33)

Related Items (7)

Certain fractional formulas of the extended \(k\)-hypergeometric functions ⋮ A new weighted fractional operator with respect to another function via a new modified generalized Mittag-Leffler law ⋮ Fractional version of Ostrowski-type inequalities for strongly \(p\)-convex stochastic processes via a \(k\)-fractional Hilfer-Katugampola derivative ⋮ Generalized derivatives and Laplace transform in (k,ψ)‐Hilfer form ⋮ A study on \(k\)-generalized \(\psi\)-Hilfer derivative operator ⋮ Investigation for the k -analogue of τ -Gauss hypergeometric matrix functions and associated fractional calculus ⋮ Ostrowski-type inequalities for \(n\)-polynomial \(\mathscr{P} \)-convex function for \(k\)-fractional Hilfer-Katugampola derivative

Cites Work

• New approach to a generalized fractional integral
• Solution of Volterra integrodifferential equations with generalized Mittag-Leffler function in the Kernels
• The \((k,s)\)-fractional calculus of \(k\)-Mittag-Leffler function
• A review of definitions for fractional derivatives and integral
• Hilfer-Katugampola fractional derivatives
• On generalized \(\mathtt{k}\)-fractional derivative operator
• \(M\)-fractional derivative under interval uncertainty: theory, properties and applications
• A new definition of fractional derivative
• (k,s)-Riemann-Liouville fractional integral and applications
• On the generalized fractional derivatives and their Caputo modification
• Existence and stability of fractional differential equations involving generalized Katugampola derivative
• On a certain extension of the Riemann-Liouville fractional derivative operator
• The k-fractional Hilfer derivative
• A further extension of the extended Riemann–Liouville fractional derivative operator
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