Results 91 to 100 of about 19,938 (283)

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

On weighted Montogomery identities for Riemann-Liouville fractional integrals

, 2012
In this paper, we extend the weighted Montogomery identities for the Riemann-Liouville fractional integrals. We also use this Montogomery identities to establish some new Ostrowski type integral inequalities.
Sarikaya, Mehmet Zeki, Yaldiz, Hatice
openaire   +2 more sources

Nonlinear Sequential Fractional Integro‐Differential Systems: Caputo‐Type Derivatives and Boundary Constraints

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In recent years, the study of sequential fractional differential equations (SFDEs) has become increasingly important in multiple domains of science and engineering. This work investigates a new class of boundary value problems (BVPs) characterized by nonlocal closed boundary conditions involving SFDEs with Caputo fractional integral operators.
Saud Fahad Aldosary, Manigandan Murugesan, Hami Gündoğdu   +2 more
wiley   +1 more source

A Novel Fractional‐Order Predictive PI Controller Approach for the Systems With Noninteger Order Delay

Optimal Control Applications and Methods, EarlyView.
Hybrid Algorithm‐Based Optimal FOPI Controller in Three‐phase UPQC system ABSTRACT Time delay (TD) is a common phenomenon in practical systems. Most studies have focused on the classical notion of integer‐order TD. However, it should not be neglected that the delay can also be noninteger.
Erdinç Şahin
wiley   +1 more source

On generalized fractional integral with multivariate Mittag-Leffler function and its applications

Alexandria Engineering Journal, 2022
The fractional calculus (FC) has been extensively studied by researchers due to its vast applications in sciences in the last few years. In fractional calculus, multivariate Mittag–Leffler functions are considered the powerful extension of the classical ...
Amna Nazir, Gauhar Rahman, Asad Ali, Saima Naheed, Kottakkaran Soopy Nisar, Wedad Albalawi, Heba Y. Zahran   +6 more
doaj   +1 more source

Contributions of the fixed point technique to solve the 2D Volterra integral equations, Riemann–Liouville fractional integrals, and Atangana–Baleanu integral operators

, 2021
In this manuscript, some fixed point results for generalized contractive type mappings under mild conditions in the setting of double controlled metric spaces (in short, η ℷ ν $\eta _{\gimel }^{\nu }$ -metric spaces) are obtained.
H. Hammad, H. Aydi, Nabil Mlaiki
semanticscholar   +1 more source

A Note on the Existence and Optimal Control of Atangana–Baleanu Fractional Stochastic Integrodifferential System With Noninstantaneous Impulses

Optimal Control Applications and Methods, EarlyView.
Optimal Control of AB Caputo Fractional Stochastic Integrodifferential Control System with Noninstantaneous Impulses. ABSTRACT This study is concerned with the existence of mild solution and optimal control for the Atangana–Baleanu fractional stochastic integrodifferential system with noninstantaneous impulses in Hilbert spaces. We verify the existence
Murugesan Johnson, Velusamy Vijayakumar, Kiwoon Kwon   +2 more
wiley   +1 more source

Wirtinger-type inequalities for Caputo fractional derivatives via Taylor’s formula

Journal of Inequalities and Applications
In this study, we firstly derive a Wirtinger-type result, which gives the connection in between the integral of square of a function and the integral of square of its Caputo fractional derivatives with the help of left-sided and right-sided fractional ...
Samet Erden, Mehmet Zeki Sarıkaya, Burçin Gokkurt Ozdemir, Neslihan Uyanık   +3 more
doaj   +1 more source

Fractional isoperimetric Noether's theorem in the Riemann-Liouville sense

, 2013
We prove Noether-type theorems for fractional isoperimetric variational problems with Riemann-Liouville derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples, in the fractional context of the calculus of variations,
Almeida, Almeida, Atanacković, Atanacković, Baleanu, Bartosiewicz, Chen, Delfim F.M. Torres, El-Nabulsi, Ferreira, Frederico, Frederico, Frederico, Frederico, Gastão S.F. Frederico, Gelfand, Herzallah, Hilfer, Jafari, Kilbas, Kiryakova, Kiryakova, Klimek, Leitmann, Malinowska, Malinowska, Malinowska, Martins, Odzijewicz, Odzijewicz, Podlubny, Pooseh, Pooseh, Riewe, Riewe, Torres, Torres, Torres, Torres, van Brunt   +39 more
core   +1 more source

Optimal Control Strategies and Continuous Dependence for Stochastic Hilfer Fractional Systems With Delay: A Volterra‐Fredholm Integro‐Differential Approach

Optimal Control Applications and Methods, EarlyView.
The graphical abstract highlights our research on Sobolev Hilfer fractional Volterra‐Fredholm integro‐differential (SHFVFI) control problems for 1<ϱ<2$$ 1<\varrho <2 $$. We begin with the Hilfer fractional derivative (HFD) of order (1,2) in Sobolev type, which leads to Volterra‐Fredholm integro‐differential equations.
Marimuthu Mohan Raja, V. Vijayakumar, Chun‐Wei Tsai, Kalyana Chakravarthy Veluvolu   +3 more
wiley   +1 more source