Abstract
In the present work, an initial value problem involving the Atangana-Baleanu derivative is considered. An explicit solution of the given problem in integral form is obtained by using the Laplace transform. The use of the given initial value problem is illustrated by considering a boundary value problem in which the solution is expressed in the form of a series expansion using an orthogonal basis obtained by separation of variables. Some examples are also given to illustrate the obtained results.
Keywords
Publication details
- DOI
- 10.24200/squjs.vol23iss2pp137-146
- Journal
- Sultan Qaboos University Journal for Science, 23(2), 137
- Publisher
- Sultan Qaboos University
- Open access
- Gold open access
- License
- CC BY 4.0
Cite this article
APA 7
S., A. M. F., S., A. S. N., & Karimov, E. T. (2018). Initial and Boundary Value Problems for Fractional Differential Equations Involving Atangana-Baleanu Derivative. Sultan Qaboos University Journal for Science, 23(2), 137. https://doi.org/10.24200/squjs.vol23iss2pp137-146
MLA 9
S., Al-Musalhi Fatma, et al. "Initial and Boundary Value Problems for Fractional Differential Equations Involving Atangana-Baleanu Derivative." Sultan Qaboos University Journal for Science, vol. 23, no. 2, 2018, pp. 137. https://doi.org/10.24200/squjs.vol23iss2pp137-146.
Chicago (author–date)
S., Al-Musalhi Fatma, Al-Salti Nasser S., and Erkinjon Tulkinovich Karimov. 2018. "Initial and Boundary Value Problems for Fractional Differential Equations Involving Atangana-Baleanu Derivative." Sultan Qaboos University Journal for Science 23 (2): 137. https://doi.org/10.24200/squjs.vol23iss2pp137-146.
Harvard
S., A. M. F., S., A. S. N. and Karimov, E. T. (2018) 'Initial and Boundary Value Problems for Fractional Differential Equations Involving Atangana-Baleanu Derivative', Sultan Qaboos University Journal for Science, 23(2), pp. 137. doi:10.24200/squjs.vol23iss2pp137-146.
Vancouver
S. AMF, S. ASN, Karimov ET. Initial and Boundary Value Problems for Fractional Differential Equations Involving Atangana-Baleanu Derivative. Sultan Qaboos University Journal for Science. 2018;23(2):137. doi:10.24200/squjs.vol23iss2pp137-146
IEEE
A. M. F. S., A. S. N. S., and E. T. Karimov, "Initial and Boundary Value Problems for Fractional Differential Equations Involving Atangana-Baleanu Derivative," Sultan Qaboos University Journal for Science, vol. 23, no. 2, pp. 137, 2018, doi: 10.24200/squjs.vol23iss2pp137-146.