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Introduction to Fractional Calculus

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Discrete Fractional Calculus

Journal home Journal issue About the journal. Keywords: fractional derivative , fractional integral , Stieltjes integral , discrete model , numerical algorithm. Published: August 31, received: November 16, Released: March 27, accepted: - [Advance Publication] Released: - corrected: -. Article overview. These early weekly meetings will be a discussion on their progress along with addressing any issues with material.

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After one or two months of this, the student will have been exposed to many different open problems, and we will proceed with one that particularly interests the student. We will continue these meetings where I will help guide them through their understanding of the open problem and encourage specific questions to investigate. Grand Engineering: Not applicable. Student Preparation Qualifications A successful student for this project should have completed real analysis and have an interest in the broad area of differential equations.

Example 5. The unique solution to the fractional initial value problem. So, applying the Sumudu transform to both sides of the fractional difference equation in 5. Considering the terms in the summation, by using the shifting formula 4. Since Sumudu transform is a one-to-one operator see [28, Theorem 3.

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Consider the initial value problem 5. Remark 5. The initial value problem 5. Consider the initial value problem. Applying the Sumudu transform to both sides of the equation and using 4. Kilbas, H.

Srivastava, and J. Samko, A. Kilbas, and O. Podlubny, Fractional Differential Equations, vol. West, M. Bologna, and P. Heymans and I.

Discrete Fractional Calculus - Dimensions

Podlubny, "Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives," Rheologica Acta, vol. Miller and B.


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Atici and P. Eloe, "A transform method in discrete fractional calculus," International Journal of Difference Equations, vol. Eloe, "Initial value problems in discrete fractional calculus," Proceedings of the American Mathematical Society, vol. Abdeljawad and D. Baleanu, "Fractional differences and integration by parts," Journal of Computational Analysis and Applications, vol.

Watugala, "Sumudu transform: a new integral transform to solve differential equations and control engineering problems," International Journal ofMathematical Education in Science and Technology, vol. Watugala, "The Sumudu transform for functions of two variables," Mathematical Engineering in Industry, vol.

Asiru, "Sumudu transform and the solution of integral equations of convolution type," International Journal of Mathematical Education in Science and Technology, vol.


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    • Kalla, "Analytical investigations of the Sumudu transform and applications to integral production equations," Mathematical Problems in Engineering, no. Belgacem and A. Karballi, "Sumudu transform fundemantal properties investigations and applications," Journal of Applied Mathematics and Stochastic Analysis, vol.

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      Kilicman and H. Belgacem, "Introducing and analysing deeper Sumudu properties," Nonlinear Studies, vol. Katatbeh and F. Belgacem, "Applications of the Sumudu transform to fractional differential equations," Nonlinear Studies, vol. Bohner and G. Hilger, "Analysis on measure chains—a unified approach to continuous and discrete calculus," Results in Mathematics, vol. Bohner and A. Holm, The theory of discrete fractional calculus: development and application [Ph.