Integral theorems pdf

Download Download PDF. Translate PDF. Applied Mathematics and Computation — www. Srivastava on the occasion of his 65th birthday Abstract In this work we will introduce theorems relating the Riemann—Liouville fractional integral and the Weyl fractional inte- gral to some well-known integral transforms including Laplace transforms, Stieltjes transforms, generalized Stieltes trans- forms, Hankel transforms, and K-transforms.

All rights reserved. Identities on fractional integrals and the Laplace transform In the following lemma, we give a relationship between the Weyl fractional integral and the Laplace transform.

Lemma 2. Using the formula [1, p. An identity on fractional integrals and the Widder potential transform In the following theorem, we give a relationship for the Riemann—Liouville fractional integral 1 and the Widder potential transform 6. Theorem 3. Substituting 34 — 36 into 18 of Theorem 2. Using the formula [2, p. Identities for various integral transforms and fractional integrals In the following lemma, we establish an identity for the Riemann—Liouville fractional integral 1 , the Stieltjes transform 7 and the generalized Stieltjes transform 8.

Lemma 4. Corollary 4. Substituting 57 and 58 in 47 of Theorem 4. Substituting 60 and 61 in 47 of Theorem 4. References [1] A. A short summary of this paper. Identities on fractional integrals and various integral transforms. Applied Mathematics and Computation — www. Srivastava on the occasion of his 65th birthday Abstract In this work we will introduce theorems relating the Riemann—Liouville fractional integral and the Weyl fractional inte- gral to some well-known integral transforms including Laplace transforms, Stieltjes transforms, generalized Stieltes trans- forms, Hankel transforms, and K-transforms.

All rights reserved. Identities on fractional integrals and the Laplace transform In the following lemma, we give a relationship between the Weyl fractional integral and the Laplace transform.

Lemma 2. Using the formula [1, p. An identity on fractional integrals and the Widder potential transform In the following theorem, we give a relationship for the Riemann—Liouville fractional integral 1 and the Widder potential transform 6.

Theorem 3. Substituting 34 — 36 into 18 of Theorem 2. Using the formula [2, p. Identities for various integral transforms and fractional integrals In the following lemma, we establish an identity for the Riemann—Liouville fractional integral 1 , the Stieltjes transform 7 and the generalized Stieltjes transform 8. Lemma 4. Corollary 4. Substituting 57 and 58 in 47 of Theorem 4.

Substituting 60 and 61 in 47 of Theorem 4.