Results 41 to 50 of about 750 (182)

Fractional Hermite–Jensen–Mercer Integral Inequalities with respect to Another Function and Application

Complexity, 2021
In this paper, authors prove new variants of Hermite–Jensen–Mercer type inequalities using ψ–Riemann–Liouville fractional integrals with respect to another function via convexity.
Saad Ihsan Butt, Muhammad Umar, Khuram Ali Khan, Artion Kashuri, Homan Emadifar   +4 more
doaj   +1 more source

Equivalences of Nonlinear Higher Order Fractional Differential Equations With Integral Equations

Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6930-6942, April 2025.
ABSTRACT Equivalences of initial value problems (IVPs) of both nonlinear higher order (Riemann–Liouville type) fractional differential equations (FDEs) and Caputo FDEs with the corresponding integral equations are studied in this paper. It is proved that the nonlinearities in the FDEs can be L1$$ {L}^1 $$‐Carathéodory with suitable conditions.
Kunquan Lan
wiley   +1 more source

Some generalized Riemann-Liouville k-fractional integral inequalities [PDF]

Journal of Inequalities and Applications, 2016
The focus of the present study is to prove some new Pólya-Szegö type integral inequalities involving the generalized Riemann-Liouville k-fractional integral operator. These inequalities are used then to establish some fractional integral inequalities of Chebyshev type.
Praveen Agarwal, Jessada Tariboon, Sotiris K. Ntouyas   +2 more
openaire   +2 more sources

Composition of Fractional Integral and Derivative Operators: Summarised in Tables

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT This paper compiles a complete, detailed list of composition properties for Riemann–Liouville fractional differintegrals, in all possible cases for orders anywhere in the complex plane, with the results presented clearly in a table for easy visual consumption.
Arran Fernandez
wiley   +1 more source

Fractional Moment Theory for Anomalous Transport: A Unified Framework for Lévy Flights, Fractals, and Complex Dynamical Systems

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT We develop a unified mathematical framework extending classical moment theory from discrete integer orders to a continuous spectrum of real orders f>0$$ f>0 $$, providing a systematic statistical characterization of complex systems exhibiting power‐law behavior.
Farrukh A. Chishtie
wiley   +1 more source

SOME PROPERTIES OF k-RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL OPERATOR

JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES, 2023
In this paper we will introduce some properties of k- Riemann Liouville fractional integral operator involving convolution property. The fractional derivative of k- Riemann Liouville fractional integral operator of integral transforms will be obtained. Applications of this operator will be introduced.
Prajapat, Radhe Shyam, Bapna, Indu Bala
openaire   +1 more source

On the Existence of Solutions of Dynamic Equations on Time Scales in Banach Spaces

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In this paper we address the question of solvability of dynamic equations on time scales in Banach spaces. In particular, our main theorem extends the result for classical differential equations in Banach spaces of Banaś and Goebel established in [5], to an arbitrary time scale.
Dušan Oberta
wiley   +1 more source

New version of midpoint-type inequalities for co-ordinated convex functions via generalized conformable integrals

Boundary Value Problems
In the current research, some midpoint-type inequalities are generalized for co-ordinated convex functions with the help of generalized conformable fractional integrals.
Mehmet Eyüp Kiriş, Miguel Vivas-Cortez, Tuğba Yalçin Uzun, Gözde Bayrak, Hüseyin Budak   +4 more
doaj   +1 more source

Certain Hermite-Hadamard type inequalities via generalized k-fractional integrals

Journal of Inequalities and Applications, 2017
Some Hermite-Hadamard type inequalities for generalized k-fractional integrals (which are also named ( k , s ) $(k,s)$ -Riemann-Liouville fractional integrals) are obtained for a fractional integral, and an important identity is established.
Praveen Agarwal, Mohamed Jleli, Muharrem Tomar   +2 more
doaj   +1 more source

Fractional Hermite-Hadamard-type inequalities for interval-valued co-ordinated convex functions

Open Mathematics, 2021
In this work, we introduce the notions about the Riemann-Liouville fractional integrals for interval-valued functions on co-ordinates. We also establish Hermite-Hadamard and some related inequalities for co-ordinated convex interval-valued functions by ...
Budak Huseyin, Kara Hasan, Ali Muhammad Aamir, Khan Sundas, Chu Yuming   +4 more
doaj   +1 more source