University of Tabriz Computational Methods for Differential Equations 2345-3982 12 1 2024 11 01 Application of fuzzy ABC fractional differential equations in infectious diseases 1 15 16440 10.22034/cmde.2023.47768.2000 EN Fatemeh Babakordi Department of Mathematics, Faculty of Science, Gonbad Kavous University, Gonbad Kavous, Iran. Tofigh Allahviranloo Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Tukey. Department of mathematics, Science and research branch, Islamic Azad university, Tehran, Iran. 0000-0002-6673-3560 Journal Article 2021 09 04 In this paper, for solving the HIV fuzzy mathematical model, it is first transformed into a system of three nonlinear fuzzy Atangana-Baleanu-Caputo (ABC) fractional differential equations with three unknowns and fuzzy initial values. Then, using the generalized Hukuhara difference and ABC fractional derivative and applying the fuzzy numerical ABC-PI method, its fuzzy solution is calculated. Moreover, some theorems are defined to prove the existence and uniqueness of the solution. Then, it is explained that the proposed method can In this paper, for solving the HIV fuzzy mathematical model, it is first transformed into a system of three nonlinear fuzzy Atangana-Baleanu-Caputo (ABC) fractional differential equations with three unknowns and fuzzy initial values. Then, using the generalized Hukuhara difference and ABC fractional derivative and applying the fuzzy numerical ABC-PI method, its fuzzy solution is calculated. Moreover, some theorems are defined to prove the existence and uniqueness of the solution. Then, it is explained that the proposed method can be used for the system of any  equations with  unknowns.  Therefore, in order to determine the solution of the fuzzy mathematical model of the transmission of COVID-19, it is transformed into a system of six nonlinear fuzzy Atangana-Baleanu-Caputo (ABC) fractional differential equations with six unknowns and fuzzy initial values and is solved similarly. At the end, a numerical example is presented to verify the effectiveness of the proposed method.be used for the system of any equations with unknowns. Therefore, in order to determine the solution of the fuzzy mathematical model of the transmission of COVID-19, it is transformed into a system of six nonlinear fuzzy Atangana-Baleanu-Caputo (ABC) fractional differential equations with six unknowns and fuzzy initial values and is solved similarly. At the end, a numerical example is presented to verify the effectiveness of the proposed method. https://cmde.tabrizu.ac.ir/article_16440_5dc73843d9a4cf0bdafdc6d06ccb4647.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 12 1 2024 11 01 Analysis of a kernel-based method for some pricing financial options 16 30 16490 10.22034/cmde.2023.56236.2349 EN Parisa Ahmadi Balootaki Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran. Reza Khoshsiar Ghaziani Department of Mathematics, Faculty of Mathematical Science, Shahrekord University, Shahrekord, Iran. Mojtaba Fardi Department of Mathematics, Faculty of Mathematical Science, Shahrekord University, Shahrekord, Iran. Majid Tavassoli Kajani Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran. Journal Article 2023 04 17 In this paper, we propose a kernel-based method for some pricing financial options. Based on the ideas of the kernel-based approximation and finite-difference discretization, we present an efficient numerical method for solving the generalized Black-Scholes  option pricing models. Utilizing the reproducing property of kernels, we introduce an efficient framework for obtaining cardinal functions. Also, we discuss the solvability of final system to obtain some remarkable results. We provide the error estimate of the proposed kernel-based method and verify its efficiency and accuracy by numerical experiments. https://cmde.tabrizu.ac.ir/article_16490_b462323f93c14ab48fd0a86ab4ad8e77.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 12 1 2024 11 01 New generalized special functions with two generalized M-series at their kernels and solution of fractional PDEs via double Laplace transform 31 43 16751 10.22034/cmde.2023.55800.2325 EN Enes Ata Department of Mathematics, Kır¸sehir Ahi Evran University, Kır¸sehir, Turkey. 0000-0001-6893-8693 İ. Onur Kıymaz Department of Mathematics, Kır¸sehir Ahi Evran University, Kır¸sehir, Turkey. 0000-0003-2375-0202 Journal Article 2023 03 11 In this paper, we introduce three types of generalized special functions: beta, Gauss hypergeometric, and confluent hypergeometric, all involving two generalized M-series at their kernels. We then give several properties of these functions, such as integral representations, functional relations, summation relations, derivative formulas, transformation formulas, and double Laplace transforms. Furthermore, we obtain solutions of fractional partial differential equations involving these new generalized special functions and then we present graphs of the approximate behavior of the solutions. Also, we introduce a new generalized beta distribution and incomplete beta function. Finally, we establish relationships between the new generalized special functions and other generalized special functions found in the literature. https://cmde.tabrizu.ac.ir/article_16751_7023d19494e120b6533563352438c893.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 12 1 2024 11 01 The complex hyperbolic Schrodinger dynamical equation with a truncated M-fractional by using simplest equation method 44 55 16192 10.22034/cmde.2022.40084.1747 EN Asim Zafar Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Pakistan. Waseem Razzaq Math Center, House no 87 Rahmanyia colony, Vehari, Pakistan. Hadi Rezazadeh Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran. Mostafa Eslami Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran. 0000-0003-3344-5068 Journal Article 2020 05 30 This article studies a complex hyperbolic Schrodinger dynamical equation that is associated with nonlinear media via ultra short pulse propagation. The modified simplest equation method is executed to construct complex solitary wave and other solutions of the aforesaid equation by considering it in conformable M-fractional derivative sense. The acquired solutions are in the form of solitary and periodic waves and rational functions. These solutions are also described with their graphical representations by assuming appropriate values of required parameters. Moreover, the results show that the aforesaid approach can be effective for solving such nonlinear Schrodinger equations arising in nonlinear optics and physical sciences. https://cmde.tabrizu.ac.ir/article_16192_d872371bcc1e23c05065464e073d905c.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 12 1 2024 11 01 On a moving boundary problem associated with a mathematical model of breast cancer 56 66 16439 10.22034/cmde.2023.55447.2307 EN Behnam Amini Sefidab Department of Mathematics, Payame Noor University (PNU), P. O. Box: 19395-4697, Tehran, Iran. Parastoo Reihani Department of Mathematics, Payame Noor University (PNU), P. O. Box: 19395-4697, Tehran, Iran. Journal Article 2023 02 16 This paper is associated with a nonlinear parabolic moving boundary problem  raised from the mathematical modeling of the behavior of the breast avascular cancer tumors at their first stage. This model is a modification of the previous works. Using the weak form of the proposed problem, the uniqueness of the solution is proved. Based on the finite difference method, a variable time step approach is proposed to solve the problem, numerically. It is shown that the numerical approach preserves the positivity of the solution and is unconditionally stable. To show the robustness and ability of the numerical method, the numerical and exact solutions are discussed and compared for two examples with the exact solutions. https://cmde.tabrizu.ac.ir/article_16439_7877dadf8c781e21eabc8a7ccad5cb31.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 12 1 2024 11 01 Improved new qualitative results on stochastic delay differential equations of second order 67 76 15681 10.22034/cmde.2022.52821.2229 EN Cemil Tunc Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, 65080, Van, Turkey. 0000-0003-2909-8753 Zozan Oktan Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, 65080, Van, Turkey. Journal Article 2022 07 31 This paper deals with a class of stochastic delay differential equations (SDDEs) of second order with multiple delays. Here, two main and novel results are proved on stochastic asymptotic stability and stochastic boundedness of solutions of the considered SDDEs. In the proofs of results, the Lyapunov-Krasovskii functional (LKF) method is used as the main tool. A comparison between our results and those are available in the literature shows that the main results of this paper have new contributions to the related ones in the current literature. Two numerical examples are given to show the applications of the given results. https://cmde.tabrizu.ac.ir/article_15681_30c3d97eafc53dcc64c5a760003178dd.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 12 1 2024 11 01 An operational vector method based on Chebyshev wavelet and hybrid functions for Riccati differential equations: Application in nonlinear physics equations 77 88 16438 10.22034/cmde.2023.55213.2295 EN Raziyeh Dehbozorgi Iran University of science and technology, Tehran, Iran. Asiyeh Ebrahimzadeh Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran. 0000-0002-4684-7640 Journal Article 2023 02 01 In this paper, we introduce an operational vector approach that uses Chebyshev wavelets and hybrid functions to approximate the solution of the Riccati differential equation arising in nonlinear physics equations celebrated as cosmology problems. The scheme's main features include a simple structure based on certain matrices and vectors, low computational complexity, and high accuracy. The method is direct, which means that projection methods are not used throughout the approximation procedure in order to reduce computational cost. Error analyses are provided, and several numerical examples and comparisons confirm the proposed scheme's superiority. https://cmde.tabrizu.ac.ir/article_16438_0e2e2f43f5758282d8b0f287ab46ef64.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 12 1 2024 11 01 Existence and uniqueness results for generalized fractional integrodifferential equations with nonlocal terminal condition 89 99 16489 10.22034/cmde.2023.53224.2243 EN Vinod Vijaykumar Kharat Department of Mathematics, N. B. N. Sinhgad College of Engineering, Kegaon-Solapur-413255, India. Anand Rajshekhar Reshimkar Department of Mathematics, D. B. F. Dayanand College of Arts and Science, Solapur-413002, India. Mansoorali A Kazi Department of Mathematics, N. B. N. Sinhgad College of Engineering, Kegaon-Solapur-413255, India. Machchhindra Tolaji Gophane Department of Mathematics, Shivaji University, Kolhapur-416004, India. Journal Article 2022 08 30 In this study, we give results on the existence and uniqueness of solutions for generalized fractional integrodifferential equations with a nonlocal terminal condition. We have proved the existence of solutions to the problem proposed using the Schauder fixed point theorem and the uniqueness of its solutions is proved using the Banach fixed point theorem. At the end, we discussed the examples to support our results. https://cmde.tabrizu.ac.ir/article_16489_36a6c18ef37bab6bb10a8675fc3e2427.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 12 1 2024 11 01 Existence, uniqueness, and stability analysis of coupled random fractional boundary value problems with nonlocal conditions 100 116 16437 10.22034/cmde.2023.53235.2246 EN Khuddush Mahammad Department of Mathematics, Dr. Lankapalli Bullayya College of Engineering, Resapuvanipalem, Visakhapatnam, 530013, Andhra Pradesh, India. 0000-0002-1236-8334 Mohammed Benyoub Department of Mathematics, Ecole Normale Sup\'{e}rieure, Taleb Abderrahmane de Laghouat, 03000 Laghouat, Algeria. Sarmila Kathun Department of Applied Mathematics, Andhra University, Visakhapatnam, 530003, India. Journal Article 2022 08 31 In this paper, the existence, uniqueness, compactness, and stability of a coupled random differential equations involving the Hilfer fractional derivatives with nonlocal boundary conditions are discussed. Arguments are discussed via some random fixed point theorems in a separable vector Banach spaces and Ulam type stability. Some examples are presented to ensure the abstract results. https://cmde.tabrizu.ac.ir/article_16437_de9a4fff6969102ef7c4f91af3eb3c81.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 12 1 2024 11 01 A one-step algorithm for strongly non-linear full fractional duffing equations 117 135 16317 10.22034/cmde.2023.53596.2256 EN Jafar Biazar Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 41335-1914, P.C.4193822697, Rasht, Iran. 0000-0001-8026-2999 Hamed Ebrahimi Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 41335-1914, P.C.4193822697, Rasht, Iran. 0000-0003-0462-4729 Journal Article 2022 09 27 In the current study, a one-step numerical algorithm is presented to solve strongly non-linear full fractional duffing equations. A new fractional-order operational matrix of integration via  quasi-hat functions (QHFs) is introduced. Utilizing the operational matrices of QHFs, the main problem will be transformed into  a number of univariate polynomial equations. Absolute errors of the results in approximations and convergence analysis are addressed. Ultimately, five examples are provided to illustrate the capabilities of this algorithm. The numerical results are illustrated in some Tables and Figures, for different values of the parameters $\alpha~ and~ \beta$. https://cmde.tabrizu.ac.ir/article_16317_6b1d2c3cf524ceb9b297eec09829c912.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 12 1 2024 11 01 Almost sure exponential numerical stability of balanced Maruyama with two step approximations of stochastic time delay Hopfield neural networks 136 148 16455 10.22034/cmde.2023.55861.2330 EN Sivarajan Kopperundevi Department of Mathematics, Dr. M.G.R Educational and Research Institute(To be Deemed), Maduravoyal, Chennai-600 095, India. Journal Article 2023 03 15 This study examines the balanced Maruyama with two step approximations of stochastic Hopfield neural networks with delay. The main aim of this paper is to discover the conditions under which the exact solutions remain stable for the balanced Maruyama with two-step approximations of stochastic delay Hopfield neural networks (SDHNN). The semi martingale theorem for convergence is used to demonstrate the almost sure exponential stability of balanced Maruyama with two-step approximations of stochastic delay Hopfield networks. Additionally, the numerical balanced Euler approximation's stability conditions are compared. Our theoretical findings are illustrated with numerical experiments. https://cmde.tabrizu.ac.ir/article_16455_1d9d27cd91712d1c8b35c7161b3fea7a.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 12 1 2024 11 01 Numerical simulation of two link robotic manipulator with white and colored noise 149 158 16129 10.22034/cmde.2023.54929.2283 EN Hadiseh Babazadeh Faculty of Electrical Engineering, Urmia University of Technology, Urmia, Iran. Parisa Nabati Faculty of Science, Urmia University of Technology, Urmia, Iran. Journal Article 2023 01 12 The main purpose of this paper is to introduce a new method to analyze the effects of the white and colored noise perturbations on the robotic arms. To show the efficiency of the presented idea the simplest manipulator, two link robotic arm, is considered. Most previous noise analyses of manipulators are done using mechanical or electrical modeling. Applying exact kinematic equations of the robots is the novelty of the proposed research. For this purpose, by adding white and colored noise terms in each angle function of the robotic arm, the end effector linear velocity is studied. Also, mechanical variation's effect on the final velocity in noisy space is considered. The longer the length of the links, the more the noise effect. Analysis of simulation results shows that the root mean square error in 2nd order is more than when angle functions are of the first order. Also, the mean square error is less when colored noise is added in comparison to the white noise. The Matlab programming is used to perform numerical examples to show the efficiency and accuracy of the presented idea. https://cmde.tabrizu.ac.ir/article_16129_3d3aff4f3097056e2e0d763f91fbe479.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 12 1 2024 11 01 Srivastava-Luo-Raina M-transform involving the incomplete I-functions 159 172 16434 10.22034/cmde.2023.55721.2322 EN Sanjay Bhatter Department of Mathematics, Malaviya National Institute of Technology Jaipur, India. Nishant - Department of Mathematics, Malaviya National Institute of Technology Jaipur, India. Shyamsunder - Department of Mathematics, Malaviya National Institute of Technology Jaipur, India. 0000-0002-8020-0541 Sunil Dutt Purohit Department of Mathematics, Faculty of Science, Rajsthan Technical University, India. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon. 0000-0002-1098-5961 Journal Article 2023 03 06 In this article, the Srivastava-Luo-Raina $M$-transform is applied to establish the image formula for the multiplication of a family of polynomials and the incomplete $I$-functions. Additionally, we discovered the image formulations for a few significant and valuable cases of incomplete $I$-functions. The conclusions drawn in this study are general in nature, and by assigning specific values to the parameters involved in the primary conclusions, numerous previously discovered and few undiscovered conclusions can be achieved. https://cmde.tabrizu.ac.ir/article_16434_a8cf32a3a1610d21ab0511a49d8ec5b2.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 12 1 2024 11 01 An efficient adaptive wavelet method for pricing time-fractional American option variational inequality 173 188 16347 10.22034/cmde.2023.54659.2277 EN Hosein Pourbashash Department of Mathematics, University of Garmsar, Garmsar, Iran. Mahmood Khaksar-e Oshagh Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran. Somayyeh Asadollahi Faculty of Management and Accounting, College of Farabi, Tehran University, Qom, Iran. Journal Article 2022 12 27 Based on the time-fractional  Black-Scholes pricing model, the evaluation of an American-style option problem  can be formulated as  a   free boundary problem.  It is equivalent  to a time-fractional parabolic variational inequality. Due to the time-fractional derivative involved in  the problem, increasing the computational cost for large final times has been expected in  the numerical   solution for this problem. In this paper, we want to propose a new adaptive numerical method to solve   this problem   accurately, with low computational cost. The presented method is based on interpolating wavelets family. An adaptive scheme in time discretization with an adaptive wavelet collocation method for space discretization has been used for  the given problem. We show  that combination of interpolating wavelet basis and finite difference method, makes an accurate structure to design an optimal adaptive mesh  for this problem. The presented computational mesh  by this method can prevent growing of computational cost by time. The  performance of the proposed method has been tested by means of some numerical experiments. We show that,  in comparison with the full grid algorithms, the presented adaptive algorithm can capture the priori unknown free boundary and is able to find the value of American put option price with high accuracy and reasonable CPU time. https://cmde.tabrizu.ac.ir/article_16347_6dfcbc6c197f0b10d2e5cfa91eec03d7.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 12 1 2024 11 01 Solution of Volterra integral equations of the first kind with discontinuous kernels by using the Adomian decomposition method 189 195 16433 10.22034/cmde.2023.52806.2227 EN Simin Aghaei Amirkhizi Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran Yaghoub Mahmoudi Department of Mathematics, Tabriz Branch Islamic Azad University, Tabriz, Iran Ali Salimi Shamloo Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran Journal Article 2022 07 30 In this paper, for solving linear and nonlinear Volterra integral equations of the first kind with discontinuous kernels, the Adomian decomposition method, and the modified Adomian decomposition method are presented. We convert  the  main equation into the  Volterra integral equation of the second kind. The numerical examples are given to denote the accuracy of the suggested method. https://cmde.tabrizu.ac.ir/article_16433_26ad8ae9ca739354f5852798b61c83c7.pdf