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Generalized fractional operator with applications in mathematical physics

Author

Listed:
  • Samraiz, Muhammad
  • Mehmood, Ahsan
  • Iqbal, Sajid
  • Naheed, Saima
  • Rahman, Gauhar
  • Chu, Yu-Ming

Abstract

In this paper, we establish a generalize weighted fractional derivative operator involving Mittag-Leffler function in its kernel. This new operator generalizes some well known operators like the Prabhakar fractional derivative. Some significant characteristics of the newly established operator are studied. The weighted fractional derivative and inverse integral of extended hypergeometric function are evaluated. The weighted Laplace transform of fractional derivative operator is obtained. The relationship between weighted and classical Laplace is proved by presenting some examples. The solution of the fractional kinetic differintegral equation is expressed as a series involving the Mittag-Leffler function. The growth model with graphical representation is provided as applications in engineering.

Suggested Citation

  • Samraiz, Muhammad & Mehmood, Ahsan & Iqbal, Sajid & Naheed, Saima & Rahman, Gauhar & Chu, Yu-Ming, 2022. "Generalized fractional operator with applications in mathematical physics," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p2:s0960077922010098
    DOI: 10.1016/j.chaos.2022.112830
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    References listed on IDEAS

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    1. Fernandez, Arran & Özarslan, Mehmet Ali & Baleanu, Dumitru, 2019. "On fractional calculus with general analytic kernels," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 248-265.
    2. Zhao, Dazhi & Luo, Maokang, 2019. "Representations of acting processes and memory effects: General fractional derivative and its application to theory of heat conduction with finite wave speeds," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 531-544.
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