Exponential Operators For Generalized Lamb–Bateman Singular Integral Equations

In this article, the author extends the application of exponential operators to solve certain non-linear fractional differential equation, space fractional partial differential equation and two dimensional Lamb– Bateman singular integral equation. Numerous constructive examples and exercises presented throughout the paper. The main purpose of this work is to present mathematical results that are useful to researchers in a variety of fields.

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  • [1] Aghili, A., New results involving Airy polynomials, fractional calculus and solution to generalized heat equation, New trends in mathematical sciences, 3 (2015).
  • [2] Aghili, A., Fractional Black–Scholes equation, International Journal of Financial Engineering, 4 (1) (2017) World Scientific Publishing Company, DOI: 10.1142/S2424786317500049.
  • [3] Apelblat, A., Laplace transforms and their applications, Nova Science Publishers Inc., New York, 2012.
  • [4] Babusci, D., Dattoli, G., Sacchetti, D., The Lamb-–Bateman Integral Equation and the Fractional Derivatives, Fractional calculus and applied analysis, 14 (2) (2011), 317–320.
  • [5] Dattoli, G., Operational methods, fractional operators and special polynomials. Applied Mathematics and Computations, 141 (2003) 151–159.
  • [6] Dattoli, G., Srivastava, H.M., Zhukovsky, K.V., Operational methods and differential equations to initial value problems. Applied Mathematics and computations, 184 (2007) 979–1001.