SEMI-ANALYTICAL ITERATIVE METHODS FOR SOLVING TIME-FRACTIONAL RICCATI DIFFERENTIAL EQUATION

KAZEEM IYANDA FALADE; KOLAWOLE ADEFEMI  ADEYEMO; NURU  MUAZU; SAFIU AJAYI RAIFU; VICTORIA IYADUNNI AYODELE; OLUBUSAYO VICTORIA BABATUNDE; BASHIRAT OMOBOLAJI ABDULLAHI

KAZEEM IYANDA FALADE DEPARTMENT OF MATHEMATICS, ALIKO DANKOTE UNIVERISTY OF SCIENCE AND TECHNOLOGY, WUDIL KANO STATE NIGERIA.
KOLAWOLE ADEFEMI ADEYEMO DEPARTMENT OF COMPUTER AND MATHEMATICS, NIGERIA POLICE ACADEMY, WUDIL KANO STATE NIGERIA.
NURU MUAZU DEPARTMENT OF MATHEMATICS, ALIKO DANKOTE UNIVERISTY OF SCIENCE AND TECHNOLOGY, WUDIL KANO STATE NIGERIA.
SAFIU AJAYI RAIFU DEPARTMENT OF COMPUTER AND MATHEMATICS, NIGERIA POLICE ACADEMY, WUDIL KANO STATE NIGERIA.
VICTORIA IYADUNNI AYODELE DEPARTMENT OF COMPUTER AND MATHEMATICS, NIGERIA POLICE ACADEMY, WUDIL KANO STATE NIGERIA.
OLUBUSAYO VICTORIA BABATUNDE DEPARTMENT OF MATHEMATICS, FACULTY OF PHYSICAL SCIENCES, UNIVERSITY OF ILORIN, ILORIN KWARA STATE NIGERIA.
BASHIRAT OMOBOLAJI ABDULLAHI MATHEMATICS UNIT, MIMBAR COLLEGE, AGODI, IBADAN, OYO STATE, NIGERIA.

Keywords: Fractional Riccati differential equation, analytical and iterative, modified new iterative method (MNIM), homotopy perturbation method (HPM)

Abstract

In this paper, two semi-analytical methods for solving the time-fractional Riccati differential equation, the homotopy perturbation method (HPM) and the modified new iterative method (MNIM), are employed to solve the time-fractional Riccati equation, which is characterized by its nonlinear and fractional-order nature, and serves as a fundamental model in mathematical physics and engineering processes involving memory and hereditary properties. By incorporating the Caputo fractional derivative, the study captures the nonlocal temporal dynamics of the system. The MNIM is formulated to enhance convergence and minimize computational complexity, while HPM is utilized to construct an approximate analytical series solution without linearization or discretization. Both methods yield rapidly convergent series solutions that approximate the exact analytical solution with high accuracy. We considered two test cases, and the results demonstrated the efficiency, simplicity, and robustness of the proposed methods for various fractional orders, establishing both methods as powerful tools for fractional nonlinear differential equations in applied sciences and engineering. The paper lies in applying semi-analytical iterative methods tailored to the time-fractional Riccati differential equation, providing accurate approximate solutions with reduced computational complexity.

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