Fractional order differential and integral equations with Erdélyi‐Kober operators: Explicit solutions by means of the transmutation method

机译：与Erdélyi-kober运算符的分数级差分和整体方程：通过嬗变方法显式解决方案

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By means of the transmutation method we construct explicit solutions of some fractional order Volterra integral equations of second kind, with one or two different Erdélyi‐Kober operators, the latter involving hypergeometric integrals. The same method is applied to fractional differential and differ‐integral equations, involving simultaneously Erdélyi‐Kober fractional integrals and derivatives of different orders. The idea of this method is to use transmutation operators to reduce the solutions of the discussed problems to the known solutions of the simplest problems of the same type (in this case, with Riemann‐Lioville operators). Some illustrative examples are given.

机译：通过嬗变方法，我们构建了第二种分数阶Volterra积分方程的明确解决方案，其中一个或两个不同的Erdélyi-kober运算符，后者涉及超距离积分。相同的方法应用于分数差分和不同积分方程，涉及同时埃尔德利 - 甘蔗的分数积分和不同订单的衍生物。这种方法的思想是使用嬗变运营商将讨论的问题的解决方案减少到相同类型的最简单问题的已知解决方案（在这种情况下，用黎曼 - Lioville运算符）。给出了一些说明性的例子。

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《International Conference "Applications of Mathematics in Engineering and Economics"》|2011年||共12页
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Virginia S. Kiryakova;
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中图分类 TB112-532;
关键词
fractional order differential equations; Volterra integral equations of second kind; transmutation method; fractional calculus; Mittag-Leffler function;

机译：分数级微分方程;二种volterra积分方程;嬗变方法;分形微分;mittag-leffler函数;

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1. Existence of solutions for Riemann-Liouville fractional differential equations with nonlocal Erdélyi-Kober integral boundary conditions on the half-line [J] . Phollakrit Thiramanus, Sotiris K Ntouyas, Jessada Tariboon Boundary value problems . 2015,第1期

机译：半线上具有非局部Erdélyi-Kober积分边界条件的Riemann-Liouville分数阶微分方程解的存在性
2. Numerical schemes for integro-differential equations with Erd,lyi-Kober fractional operator [J] . Plociniczak Lukasz, Sobieszek Szymon Numerical algorithms . 2017,第1期

机译：ERD，LYI-KOBER FRACTIONATION ORD INTECTO微分方程数值方案
3. Existence, uniqueness and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order [J] . JinRong Wang, Chun Zhu, Michal Fěckan Central European Journal of Physics . 2013,第6期

机译：分数阶二次Erdélyi-Kober型积分方程解的存在性，唯一性和极限性质
4. Fractional order differential and integral equations with Erdélyi‐Kober operators: Explicit solutions by means of the transmutation method [C] . Virginia S. Kiryakova International Conference "Applications of Mathematics in Engineering and Economics" . 2011

机译：与Erdélyi-kober运算符的分数级差分和整体方程：通过嬗变方法显式解决方案
5. Numerical solution of linear transport equations with scattering operators of integral and differential type. [D] . Phillips, Kevin Gregory. 2008

机译：具有积分和微分类型散射算子的线性传输方程的数值解。
6. Certain Inequalities Involving Generalized Erdélyi-Kober Fractional q-Integral Operators [O] . Praveen Agarwal, Soheil Salahshour, Sotiris K. Ntouyas, -1

机译：涉及广义Erdélyi-Kober分数阶q-积分算子的某些不等式
7. Existence of solutions for Riemann-Liouville fractional differential equations with nonlocal Erdélyi-Kober integral boundary conditions on the half-line [O] . 2015

机译：半线上具有非局部Erdélyi-Kober积分边界条件的Riemann-Liouville分数阶微分方程解的存在性
8. The Numerical Solution of Parabolic Partial Differential Equations by the Method of Integral Operators. [R] . Colton, D., Chang, Y. F. 1977

机译：用积分算子法求解抛物型偏微分方程的数值解。

Fractional order differential and integral equations with Erdélyi‐Kober operators: Explicit solutions by means of the transmutation method

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