In our work, we derived the fractional order q-integrals and q-derivatives concerning a basic analogue to the Aleph-function of two variables (AFTV). We discussed a related application and the q-extension of the corresponding ...
This paper is concerned with the existence of the solution to mixed-type non-linear fractional functional integral equations involving generalized proportional ((Formula presented.))-Riemann–Liouville along with Erdélyi–Kober ...
The main goal of this manuscript is to investigate a fractional optimal control problem subject to a dynamical system involving Hadamard fractional derivatives. Necessary conditions for the optimality of the considered ...
Baleanu, Dumitru; Agarwal, Ravi P; Khan, Hasib; Khan, Rahmat Ali; Jafari, Hossein(2015-12-01)
In this paper, we deal with a fractional differential equation of order δ1∈(3,4] with initial and boundary conditions, (Formula Presented), addressing the existence of a positive solution (EPS), where the fractional ...
Efficient thermal transportation in compact heat density gadgets is a prevailing issue to be addressed. The flow of a mono nanofluid (SiO2/Kerosene oil) and hybrid nanofluid (TiO2 + SiO2/Kerosene oil) is studied in context ...
The objective of this paper is to introduce the discrete Laplace transform. Basic theorems related to this transformation are mentioned and the discrete Laplace transform of basic functions are given.
The purpose of this study is to employ the Sine–Cosine expansion approach to produce some new sort of soliton solutions for the cubic–quintic nonlinear Helmholtz problem. The nonlinear complex model compensates for backward ...
Abuelela, Waleed; El-Deeb, Ahmed A.; Baleanu, Dumitru(2022-11)
Throughout this article, generalizations of some Grónwall–Bellman integral inequalities for two real-valued unknown functions in n independent variables are introduced. We are looking at some novel explicit bounds of a ...
This work aims to share some fractional integrals and derivatives containing three real parameters. The main
tool to introduce such operators is the corresponding Abel’s equation. Solvability conditions for the Abel’s ...
Numerical calculation of the fractional integrals and derivatives is the code to
search fractional calculus and solve fractional differential equations. The exact
solutions to fractional differential equations are ...
In this paper, we consider the stiff systems of ordinary differential equations arising from chemistry kinetics. We develop the fractional order model for chemistry kinetics problems by using the new fractal operator such ...
El-Owaidy, Hassan M.; El-Deeb, Ahmed A.; Makharesh, Samer D.; Baleanu, Dumitru; Cesarano, Clement(2022-07)
In this important work, we discuss some novel Hilbert-type dynamic inequalities on time scales. The inequalities investigated here generalize several known dynamic inequalities on time scales and unify and extend some ...
Al-Jamel, Ahmed; Al-Masaeed, Mohamed; Rabei, Eqab. M.; Baleanu, Dumitru(2022-09)
In this paper, the deformation of special relativity within the frame of conformable derivative is formulated. Within this context, the two postulates of the theory are re-stated. Then, the addition of velocity laws are ...
In wave theory, the higher dimensional non-linear models are very important to define the physical phenomena of waves. Herein study we have built the various solitons solutions of (4+1)- dimensional fractional-order Fokas ...
This paper is devoted to introduce a way of construction of the well-defined boundary conditions for the solutions of a singular fifth-order equation with deficiency indices (5, 5). Imposing suitable separated and coupled ...
Firoozjaee, Mohammad Arab; Jafari, Hossein; Johnston, Sarah Jane; Baleanu, Dumitru(2022-12-01)
We apply the Ritz method to approximate the solution of optimal control problems through the use of polynomials. The constraints of the problem take the form of differential equations of fractional order accompanied by the ...
The present research investigates the Susceptible-Infected-Recovered (SIR) epidemic model of childhood diseases and its complications with the Atangana-Baleanu fractional derivative operator in the Caputo sense (ABC). With ...
The main aim of the present article is to introduce some new ∇-conformable dynamic inequalities of Hardy type on time scales. We present and prove several results using chain rule and Fubini’s theorem on time scales. Our ...