Global Journal of Science Frontier Research, F: Mathematics and Decision Science, Volume 23 Issue 4

Let λ= ʋt, dλ = ʋdt put these values in eq.(2.6) then Z { ∗ } = 1 ʋ ∫ −λ/ʋ ∞ 0 [∫ ( ) (λ − ) λ 0 ] λ/ʋ = 1 ʋ 2 ∫ ∫ − λ ʋ λ 0 ∞ 0 ( ) (λ − ) λ … (2.7) Put γ= λ -τ, dγ = dλ in eq. (2.7) since the variable τ is constant hence when we integrate with respect to τ, we get Z { ∗ } = 1 ʋ 2 ∫ ∫ − + ʋ ∞ 0 ∞ 0 ( ) ( ) = 1 ʋ 2 ∫ − ʋ ∞ 0 ( ) . ∫ − ʋ ∞ 0 ( ) … (2.8) = ʋ = ʋ ℎ ℎ = ʋ = ʋ = 1 ʋ 2 [∫ − ∞ 0 ʋ (ʋ ) ] [∫ − ʋ (ʋ ) ∞ 0 ] { ∗ } = ∫ −∞ 0 (ʋ ) . ∫ − (ʋ ) ∞ 0 { ∗ } = ʋ 2 { }. { } If the function { } and { ′ } are well defined then First derivative { ′( )} = 1 ʋ ́ ∫ − ́ ∞ 0 (ʋ ) A New Integral Transform Called “Saxena & Gupta Transform” and Relation between New Transform and other Integral Transforms 1 Year 2023 13 Frontier Research Volume XXIII Issue ersion I V ( F ) Science © 2023 Global Journals Global Journal of The New Transform of Derivative and Integral Derivative property: IV N otes iv)