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1. Efficient spectral collocation method for nonlinear systems of fractional pantograph delay differential equations.

Author

Zaky, M. A., Babatin, M., Hammad, M., Akgül, A., and Hendy, A. S.

Subjects
COLLOCATION methods, PANTOGRAPH, FRACTIONAL differential equations, NONLINEAR systems, FRACTIONAL calculus, DELAY differential equations, LOGARITHMIC functions, HAMILTON-Jacobi equations
Abstract

Caputo-Hadamard-type fractional calculus involves the logarithmic function of an arbitrary exponent as its convolutional kernel, which causes challenges in numerical approximations. In this paper, we construct and analyze a spectral collocation approach using mapped Jacobi functions as basis functions and construct an efficient algorithm to solve systems of fractional pantograph delay differential equations involving Caputo-Hadamard fractional derivatives. What we study is the error estimates of the derived method. In addition, we tabulate numerical results to support our theoretical analysis. [ABSTRACT FROM AUTHOR]

Published
2024
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