Browsing by Author "Akgül, Ali"

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Citation - WoS: 1
Citation - Scopus: 1
The Extended Laguerre Polynomials {aq,n ^(a)} (X) Involving Q^fq, Q > 2
(Wiley, 2022) Kalim, Muhammad; Akguel, Ali; Jarad, Fahd; Khan, Adnan; Akgül, Ali
In this paper, for the proposed extended Laguerre polynomials {A(q,n )((alpha))}, the generalized hypergeometric function of the type (F)(q)(q), q > 2 and extension of the Laguerre polynomial are introduced. Similar to those related to the Laguerre polynomials, the generating function, recurrence relations, and Rodrigue's formula are determined. Some corollaries are also discussed at the end.
On Solutions of Variable-Order Fractional Differential Equations
(2017) Akgül, Ali; Inc, Mustafa; Baleanu, Dumitru
Numerical calculation of the fractional integrals and derivatives is the code tosearch fractional calculus and solve fractional differential equations. The exactsolutions to fractional differential equations are compelling to get in real ap-plications, due to the nonlocality and complexity of the fractional differentialoperators, especially for variable-order fractional differential equations. There-fore, it is significant to enhance numerical methods for fractional differentialequations. In this work, we consider variable-order fractional differential equa-tions by reproducing kernel method. There has been much attention in theuse of reproducing kernels for the solutions to many problems in the recentyears. We give an example to demonstrate how efficiently our theory can beimplemented in practice.
Citation - WoS: 10
Citation - Scopus: 11
Optimal Variational Iteration Method for Parametric Boundary Value Problem
(Amer inst Mathematical Sciences-aims, 2022) Nadeem, Muhammad; Karim, Shazia; Akguel, Ali; Jarad, Fahd; Ain, Qura Tul; Akgül, Ali
Mathematical applications in engineering have a long history. One of the most well-known analytical techniques, the optimal variational iteration method (OVIM), is utilized to construct a quick and accurate algorithm for a special fourth-order ordinary initial value problem. Many researchers have discussed the problem involving a parameter c. We solve the parametric boundary value problem that can't be addressed using conventional analytical methods for greater values of c using a new method and a convergence control parameter h. We achieve a convergent solution no matter how huge c is. For the approximation of the convergence control parameter h, two strategies have been discussed. The advantages of one technique over another have been demonstrated. Optimal variational iteration method can be seen as an effective technique to solve parametric boundary value problem.
Citation - WoS: 31
Citation - Scopus: 34
Theoretical and Numerical Analysis of Fractal Fractional Model of Tumor-Immune Interaction With Two Different Kernels
(Elsevier, 2022) Ahmad, Shabir; Ullah, Aman; Akgu, Ali; Baleanu, Dumitru; Akgül, Ali
Fractal fractional operators in Caputo and Caputo-Fabrizio sense are being used in this manuscript to explore the interaction between the immune system and cancer cells. The tumour-immune model has been investigated numerically and theoretically by the singular and nonsingular fractal fractional operators. Via fixed point theorems, the existence and uniqueness of the model under the Caputo fractal fractional operator have been demonstrated. Using the fixed point theory, the existence of a unique solution has been derived under the Caputo-Fabrizio case. Through nonlinear analysis, the Ulam-Hyres stability of the model has been derived. For the singular and nonsingular fractal fractional operators, numerical results have been developed by Lagrangian-piece wise interpolation. We simulate the numerical results for the various sets of fractional and fractal orders to describe the relationship between immune and cancer cells under the novel operators with two different kernels. We compared the dynamics of the tumor-immune model using a power law and an exponential-decay kernel to explore that the nonsingular fractal fractional operator provides better dynamics for the considered model. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University