Results 41 to 50 of about 623 (167)

The mean value theorem and Taylor's theorem for fractional derivatives with Mittag-Leffler kernel. [PDF]

, 2018
We establish analogues of the mean value theorem and Taylor’s theorem for fractional differential operators defined using a Mittag-Leffler kernel.
Baleanu, Dumitru, Fernandez, Arran
core   +2 more sources

New Generalized the Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals [PDF]

Symmetry, 2020
In this paper, a new identity for the generalized fractional integral is defined, through which new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established.
Ohud Almutairi, Adem Kiliçman
openaire   +1 more source

The Approximate Analytic Solution of the Time-Fractional Black-Scholes Equation with a European Option Based on the Katugampola Fractional Derivative

Mathematics, 2021
In the finance market, it is well known that the price change of the underlying fractal transmission system can be modeled with the Black-Scholes equation.
Sivaporn Ampun, Panumart Sawangtong
doaj   +1 more source

Mellin Transforms of the Generalized Fractional Integrals and Derivatives

, 2014
We obtain the Mellin transforms of the generalized fractional integrals and derivatives that generalize the Riemann-Liouville and the Hadamard fractional integrals and derivatives.
Bucchianico, Butkovskii, Butzer, Butzer, Butzer, Butzer, Bóna, Erdélyi, Erdélyi, Flajolet, Gaboury, Goldman, Hadamard, Herrmann, Katugampola, Katugampola, Kilbas, Kilbas, Kilbas, Kilbas, Kiryakova, Machado, Miller, Noor, Noor, Noor, Odzijewicz, Odzijewicz, Odzijewicz, Oldham, Podlubny, Pooseh, Robbins, Robinson, Rodrigues, Roman, Roman, Roman, Rota, Rota, Samko, Udita N. Katugampola, Yakubovich   +42 more
core   +1 more source

Bounds for the Remainder in Simpson’s Inequality via n-Polynomial Convex Functions of Higher Order Using Katugampola Fractional Integrals

Journal of Mathematics, 2020
The goal of this paper is to derive some new variants of Simpson’s inequality using the class of n-polynomial convex functions of higher order. To obtain the main results of the paper, we first derive a new generalized fractional integral identity ...
Yu-Ming Chu, Muhammad Uzair Awan, Muhammad Zakria Javad, Awais Gul Khan   +3 more
doaj   +1 more source

Certain new weighted estimates proposing generalized proportional fractional operator in another sense

Advances in Difference Equations, 2020
The present work investigates the applicability and effectiveness of generalized proportional fractional integral ( GPFI $\mathcal{GPFI}$ ) operator in another sense.
Thabet Abdeljawad, Saima Rashid, A. A. El-Deeb, Zakia Hammouch, Yu-Ming Chu   +4 more
doaj   +1 more source

On the weighted fractional integral inequalities for Chebyshev functionals

Advances in Difference Equations, 2021
The goal of this present paper is to study some new inequalities for a class of differentiable functions connected with Chebyshev’s functionals by utilizing a fractional generalized weighted fractional integral involving another function G $\mathcal{G ...
Gauhar Rahman, Kottakkaran Sooppy Nisar, Sami Ullah Khan, Dumitru Baleanu, V. Vijayakumar   +4 more
doaj   +1 more source

The general Caputo–Katugampola fractional derivative and numerical approach for solving the fractional differential equations

Alexandria Engineering Journal
In this manuscript, we present the general fractional derivative (FD) along with its fractional integral (FI), specifically the ψ-Caputo–Katugampola fractional derivative (ψ-CKFD).
Lakhlifa Sadek, Sahar Ahmed ldris, Fahd Jarad   +2 more
doaj   +1 more source

Some inequalities obtained by fractional integrals of positive real orders

Journal of Inequalities and Applications, 2020
The primary objective of this study is to handle new generalized Hermite–Hadamard type inequalities with the help of the Katugampola fractional integral operator, which generalizes the Hadamard and Riemann–Liouville fractional integral operators into one
Mustafa Gürbüz, Yakup Taşdan, Erhan Set   +2 more
doaj   +1 more source

Generalized Taylor formulas involving generalized fractional derivatives

, 2017
In this paper, we establish a generalized Taylor expansion of a given function $f$ in the form $\displaystyle{f(x) = \sum_{j=0}^m c_j^{\alpha,\rho}\left(x^\rho-a^\rho\right)^{j\alpha} + e_m(x)}$ \noindent with $m\in \mathbb{N}$, $c_j^{\alpha,\rho}\in
Benjemaa, Mondher
core   +1 more source