Browsing by Author "Agheli, Bahram"

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A method for solving nonlinear Volterra's population growth model of noninteger order
(Sprınger International Publishing, 2017) Baleanu, Dumitru; Agheli, Bahram; Firozja, M. Adabitabar; Al Qurashi, Maysaa Mohamed; 56389
Many numerical methods have been developed for nonlinear fractional integro-differential Volterra's population model (FVPG). In these methods, to approximate a function on a particular interval, only a restricted number of points have been employed. In this research, we show that it is possible to use the fuzzy transform method (F-transform) to tackle with FVPG. It makes the F-transform preferable to other methods since it can make full use of all points on this interval. We also make a comparison showing that this method is less computational and is more convenient to be utilized for coping with nonlinear integro-differential equation (IDEs), fractional nonlinear integro-differential equation (FIDEs), and fractional ordinary differential equations (FODEs).
An optimal method for approximating the delay differential equations of noninteger order
(Springer Open, 2018) Baleanu, Dumitru; Agheli, Bahram; Darzi, Rahmat; 56389
The main purpose of this paper is to use a method with a free parameter, named the optimal asymptotic homotopy method (OHAM), in order to obtain the solution of delay differential equations, delay partial differential equations, and a system of coupled delay equations featuring fractional derivative. This method is preferable to others since it has faster convergence toward homotopy perturbation method, and the convergence rate can be set as a controlled area. Various examples are given to better understand the use of this method. The approximate solutions are compared with exact solutions as well.
Analysis of the new technique to solution of fractional wave- and heat-like equation
(Jagiellonian Univ Press, 2017) Baleanu, Dumitru; Agheli, Bahram; Darzi, Rahmat; 56389
We have applied the new approach of homotopic perturbation method (NHPM) for wave- and heat-like equation featuring time-fractional derivative. A combination of NHPM and multiple fractional power series form has been used the first time to present analytical solution. In order to illustrate the simplicity and ability of the suggested approach, some specific and clear examples have been given. All computations were done using Mathematica.
Analysis of the new technique to solution of fractional wave- and heat-like equation
(Jagiellonian Univ Press, 2017) Baleanu, Dumitru; Baleanu, Dumitru; Agheli, Bahram; Darzi, Rahmat; 56389
We have applied the new approach of homotopic perturbation method (NHPM) for wave- and heat-like equation featuring time-fractional derivative. A combination of NHPM and multiple fractional power series form has been used the first time to present analytical solution. In order to illustrate the simplicity and ability of the suggested approach, some specific and clear examples have been given. All computations were done using Mathematica.
Existence Results for Langevin Equation Involving Atangana-Baleanu Fractional Operators
(2020) Baleanu, Dumitru; Darzi, Rahmat; Agheli, Bahram; 56389
A new form of nonlinear Langevin equation (NLE), featuring two derivatives of non-integer orders, is studied in this research. An existence conclusion due to the nonlinear alternative of Leray-Schauder type (LSN) for the solution is offered first and, following that, the uniqueness of solution using Banach contraction principle (BCP) is demonstrated. Eventually, the derivatives of non-integer orders are elaborated in Atangana-Baleanu sense.
Fractional advection differential equation within Caputo and Caputo-Fabrizio derivatives
(Sage Publications Ltd, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Agheli, Bahram; Al Qurashi, Maysaa Mohamed
In this research, we applied the variational homotopic perturbation method and q-homotopic analysis method to find a solution of the advection partial differential equation featuring time-fractional Caputo derivative and time-fractional Caputo-Fabrizio derivative. A detailed comparison of the obtained results was reported. All computations were done using Mathematica.
Fractional Hybrid Initial Value Problem Featuring Q-Derivatives
(Comenius Univ, 2019) Baleanu, Dumitru; Darzi, R.; Agheli, Bahram; 56389
We have perused about the existence of a solution toward hybrid initial value problem (HIVP) featuring fractional q-derivative {D-q(delta)[v(t)/h(t,v(t) max(0 <=tau <= t)vertical bar v(t)vertical bar] rho(t, v(t)), t is an element of(0,1), 0 < delta <= 1`, in which D-q(delta) denotes the Riemann-Liouville fractional q-derivative in the order of delta. In Banach algebra, by making use of a fi xed point theorem based Dhage along with mixed Lipschitz and Caratheodory condition, a way of solving the above fractional Hybrid initial value problem (FHIVP) featuring q-derivatives veri fi ed, in this study.
New study of weakly singular kernel fractional fourth-order partial integro-differential equations based on the optimum q-homotopic analysis method
(Elsevier, 2017) Baleanu, Dumitru; Baleanu, Dumitru; Darzi, Rahmat; Agheli, Bahram; 56389
In this study, the optimum q-homotopic analysis method is employed to solve fourth order partial integro-differential equations with high-order non-integer derivatives. Several specific and clear examples are also given to illustrate the simplicity and capacity of the proposed approach. All of the computations were performed using Mathematica. (C) 2017 Elsevier B.V. All rights reserved.
Population dynamic caused by war involvement via fractional derivative on time scales
(Inderscience Enterprises LTD, 2019) Baleanu, Dumitru; Baleanu, Dumitru; Neamaty, Abdolali; Agheli, Bahram; 56389
This work suggests a model for a population dynamic caused by an enemy attack to a domain of residential areas. With the help of a local non-integer order rate of change and a new structure induced on the real line, we derive a spatial discrete diffusion equation of fractional order. Then making use of the d'Alembert's change of variable we obtain a time scale which is made of union of disjoint compact intervals. These considerations lead us to a non-homogeneous second order nonlinear differential equation. The existence of a positive solution is discussed and through a numerical example the theory is illustrated.