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Table of Contents:

Chapter 1: Introduction
1.1 Background of the Study
1.2 Statement of the Problem
1.3 Research Objectives
1.4 Research Questions
1.5 Significance of the Study
1.6 Limitations of the Study
1.7 Scope of the Study

Chapter 2: Literature Review
2.1 Overview of Fractional Differential Equations
2.2 Existing Methods for Solving Fractional Differential Equations
2.3 Challenges in Solving Fractional Differential Equations
2.4 Theoretical Framework

Chapter 3: Research Methodology
3.1 Research Design
3.2 Data Collection Methods
3.3 Data Analysis Techniques
3.4 Sampling Techniques
3.5 Validation of Results

Chapter 4: Discussion of Findings
4.1 Analysis of Results
4.2 Comparison of Proposed Methods with Existing Methods
4.3 Implications of Findings
4.4 Future Research Directions

Chapter 5: Conclusion and Summary
5.1 Summary of Findings
5.2 Conclusion
5.3 Recommendations for Future Research
5.4 Contributions of the Study

Brief Overview:

The thesis on Developing new methods for solving fractional differential equations aims to address the challenges faced in solving these complex mathematical equations. Fractional differential equations have applications in various fields such as physics, engineering, and biology, but traditional methods often fall short in providing accurate solutions. This research project seeks to develop innovative methods that can effectively solve fractional differential equations and improve the accuracy and efficiency of the solutions.

The introduction chapter provides an overview of the background of the study, problem statement, research objectives, and the significance of the study. The literature review chapter presents an overview of existing methods for solving fractional differential equations, highlighting the limitations and challenges in the field. The research methodology chapter describes the research design, data collection methods, and analysis techniques employed in the study.

The discussion of findings chapter presents the analysis of results, comparisons with existing methods, and the implications of the findings. The conclusion and summary chapter summarizes the key findings, provides recommendations for future research, and highlights the contributions of the study to the field of fractional differential equations. Overall, this thesis aims to contribute to the development of new and improved methods for solving fractional differential equations, advancing the field of mathematical research.

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