Applications of Erdélyi-Kober fractional integral for solving time-fractional Tricomi-Keldysh type equation-Reference-Cited by-同舟云学术

Applications of Erdélyi-Kober fractional integral for solving time-fractional Tricomi-Keldysh type equation

Published:2020-10-01 Issue:5 Volume:23 Page:1381-1400
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Zhang Kangqun¹

Affiliation:

1. Department of Mathematics and Physics , Nanjing Institute of Technology, No. 1 Hongjing Avenue, Jiangning Science Park , Nanjing , Jiangsu , China - 211167

Abstract

Abstract In this paper we consider Cauchy problem of time-fractional Tricomi-Keldysh type equation. Based on the theory of a Erdélyi-Kober fractional integral operator, the formal solution of the inhomogeneous differential equation involving hyper-Bessel operator is presented with Mittag-Leffler function, then nonlinear equations are considered by applying Gronwall-type inequalities. At last, we establish the existence and uniqueness of L p -solution of time-fractional Tricomi-Keldysh type equation by use of Mikhlin multiplier theorem.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2020-0068/pdf

Reference35 articles.

1. M.A. Abdelkawy, E.A. Ahmed, R.T. Alqahtani, Space-time spectral collocation algorithm for solving time-fractional Tricomi-type equations. Open Phys. 14, No 1 (2016), 269–1280.

2. R.P. Agarwal, M. Meehan, D. O’Regan, Fixed Point Theory and Applications. Cambridge University Press, Cambridge (2001).

3. B. Al-Saqabi, V. Kiryakova, Explicit solutions of fractional integral and differential equations involving Erdélyi-Kober operators. Appl. Math. and Comput. 95, No 1 (1998), 1–13.

4. F. Al-Musalhi, N. Al-Salti, E. Karimov, Initial boundary value problems for a fractional differential equation with hyper Bessel operator. Fract. Calc. Appl. Anal. 21, No 1 (2018), 200–219; 10.1515/fca-2018-0013; https://www.degruyter.com/view/journals/fca/21/1/fca.21.issue-1.xml.

5. M. Antonio, F. Mainardi. A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics. Integr. Transf. Spec. Funct. 20, No 3–4 (2009), 185–198.

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Solvability of nonlinear pseudo‐parabolic equations involving generalized Caputo fractional derivatives;Mathematical Methods in the Applied Sciences;2023-06-17

2. Singular solutions of 3-D Protter-Morawetz problem for weakly hyperbolic equations of Tricomi type;“TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev;2022

3. Existence and uniqueness of analytical solution of time‐fractional Black‐Scholes type equation involving hyper‐Bessel operator;Mathematical Methods in the Applied Sciences;2021-01-17