Date of Defense
25-2-2025 4:00 PM
Location
F3-132
Document Type
Thesis Defense
Degree Name
Master of Science in Mathematics
College
COS
Department
Mathematical Sciences
First Advisor
Prof. Muhammed I. Syam
Keywords
Modified Atangana-Baleanu Fractional Derivative, Operational Matrix Method, Block Pulse Functions
Abstract
This thesis presents an analytical method to solve systems of fractional initial value problems using the Modified Atangana-Baleanu Fractional Derivative. The proposed approach leverages an improved operational matrix method, incorporating an iterative, direct computation technique to simplify the solution process and reduce computational costs. Foundational concepts in fractional calculus and block pulse functions are introduced, followed by the derivation of operational matrices tailored for fractional systems. Theoretical analysis establishes the existence and uniqueness of solutions, along with uniform convergence and error estimates. Practical examples and applications are presented that demonstrate the efficiency, accuracy, and versatility of the method in solving complex fractional problems. Both theoretical findings and numerical results validate the robustness of the proposed method, showcasing its potential to address a wide range of fractional systems efficiently.
ANALYTICAL METHOD FOR SOLVING SYSTEMS OF FRACTIONAL INITIAL VALUE PROBLEMS USING THE MODIFIED ATANGANA-BALEANU DERIVATIVE
F3-132
This thesis presents an analytical method to solve systems of fractional initial value problems using the Modified Atangana-Baleanu Fractional Derivative. The proposed approach leverages an improved operational matrix method, incorporating an iterative, direct computation technique to simplify the solution process and reduce computational costs. Foundational concepts in fractional calculus and block pulse functions are introduced, followed by the derivation of operational matrices tailored for fractional systems. Theoretical analysis establishes the existence and uniqueness of solutions, along with uniform convergence and error estimates. Practical examples and applications are presented that demonstrate the efficiency, accuracy, and versatility of the method in solving complex fractional problems. Both theoretical findings and numerical results validate the robustness of the proposed method, showcasing its potential to address a wide range of fractional systems efficiently.
